sorry about all that. Welcome to the NOVA project update. Today I'm gonna talk about what we've we've new changes and features in Rocky first and then I'm gonna tell you about what we're working on in Stein and then after that some information about like how to how to contribute how to get involved and then we'll have a little bit time for questions at the end. Firstly, what is NOVA? NOVA is a compute service. It provides the REST API and components for provisioning servers. It does both virtual machines and bare metal when used together with Ironic. NOVA has been a part of OpenStack since the Austin release. We had 255 contributors last cycle for the Rocky cycle and our latest user survey numbers adoption numbers are that 94% of deployments in production are running NOVA and that's from the 2018 user survey. So you may be aware that during Rocky we we were piloting a new review process that we were calling Rocky review runways. The basic idea behind runways is that approved blueprints could sign up in in a queue for a runway and when a blueprint goes into a runway then the idea is that the core team the core reviewers would all convene on those blueprints that are occupying runways with the idea being that we would have a little bit more organization to look at the same reviews at the same time to be more effective at completing some of these efforts that have maybe been having to be re-approved cycle to cycle. You may have experienced things like that. We also changed the spec freeze from milestone one to milestone two because of runways and the thinking behind that is that since we're using this new review process that we would allow more time for more approvals like as we complete items via runways that we would make room for more blueprints to be approved and go forward. So we've discussed we've like reflected on how did runways go for Rocky and overall I think the effect was positive. It helped complete some blueprints that had experienced repeated re-approvals over previous cycles, efforts like trusted image certificates and moving console token authorizations from the Nova console auth service to the database backend and then a little bit of stats here. These were also posted to the dev mailing list for Queens. The max number of approved blueprints we had was 53. For Rocky we approved 72 blueprints so we were very much more ambitious in the amount of work we were approving. Final completed numbers for Queens we had 42 completed we had 59 completed for Rocky but interestingly the completion percentage was similar at around 80% and we felt like that's a pretty good completion rate considering that sometimes blueprints don't get completed because like the the developer might get pulled into some higher priority stuff at their job and they may not be able to like spend all the time on on that blueprint and it may not like get completed so that 20% sort of allows for that so based on our experience in Rocky we're going to continue with the runways process in Stein same deal spec freeze at milestone 2 which is January 10th that's the at the deadline for as long as we're going to be approving new specs and blueprints so getting into the the new features for the rock lace Rocky release we we started leveraging a new neutron port binding API to minimize network downtime during live migrations another thing that you may be familiar with is that volume backed servers used to report and consume local storage on compute hosts and that is finally been fixed the new servers will no longer report the root GB usage and existing servers will be healed during move operations several Nova Network specific rest APIs were removed so we've been over time we've been working toward removing Nova Network it's been deprecated forever so this during Rocky we remove the OS fixed IPs OS floating IPs OS virtual interfaces OS F ping APIs we have a new Nova Managed DB purge command which and a new option to Nova Managed DB archive deleted rows for purge and what this will do is actually delete out the information from the shadow tables so that you get full deletion like it used to be you archive and they'll just pile up in the shadow tables now this will clear that out for you there's a new option for Nova Managed cells selvi to update cell to disable scheduling to a cell this is useful for when you want to perform maintenance on a cell and you want to take it out of the rotation you can use this Nova Managed command to disable it trusted image certificates is a new feature that is supported at as a rocky glance you can sign images using certificates and glance and then on the Nova side you can provide a list of trusted image certificate you ID's that you are saying like these are the certificates that I trust and so when you go to boot a server where you go to rebuild a server Nova will actually validate the certificate for the image with the trusted certs that you have provided so you can get extra security that way there's a new Nova Managed placement heal allocations command for caching scheduler users to pop populate placement ahead of a migration to the filter scheduler so that'll help you out if you're using the catch caching scheduler you can use this command to start populating placement with allocations and then the placement service now supports granular our back policy rules configuration so you can use the traditional policy file system to control access to placement service API's this is one of the things I mentioned earlier that benefited from runways console token off authorizations have moved from the Nova console service to the database back in and with this I wanted to show you a picture of like how the deployment topology needs to change with this so previously in Queens you had to run your console proxy globally for the deployment along with your Nova console service in Rocky because the token authorizations are stored in the cell databases instead of in the Nova console off service storage you will run your console proxies per cell and this kind of helps anyway like in a multi cell deployment deployment because that way you're not having one console proxy like have to deal with all of the traffic for your whole cluster this way you'll have them per cell here's a list of the new microversions we had in in Rocky the first one it exposes flavor extra specs in the flavors API get post input this is kind of a parody thing in that there is an extra specs API for the flavor API where you could get the extra specs but it wasn't connected to like the get and the post on the put and then also when you show server details it would show you the embedded flavors extra specs so this kind of like closes the gaps where you weren't able to get extra specs from other flavors API calls microversion 2.6 2 as the host and host ID to the instance actions get API and this is useful for being able to correlate failed instance actions with the host on which the failure occurred so this is kind of a operational improvement for people for public cloud is where it came from as I mentioned earlier trusted image certificates isn't now available in microversion 2.6 3 2.6 4 adds policy and rules to the server groups API get and post and this is kind of like adding the ability to have more advanced policy requirements for a policy so now you can do like a max servers per host rule with your anti affinity policy and this new availability of being able to associate rules with the policy that opens up the possibility of adding more in different rules as people come up with new use cases and then finally 2.6 5 adds support for reporting live migrations that are in queue to preparing status previously you can only abort a live migration if it was already running now if it's queued up and waiting and you want to cancel it you can do that so starting into what we are working on in Stein so if you're familiar with previous releases Nova cycles we used to do a thing where we would have cycle priorities a priority setting exercise for every cycle last cycle for Rocky we had thought that since we had the runway system that runways represented priorities at any given moment so we didn't really do a separate priority setting exercise but what we found at the PTG when we discussed it in the Rocky retrospective was that as a team we didn't really have it like a cohesive clarity of the types of like user facing changes that we wanted to land for the cycle so based on that discussion we decided to combine like we'll do review runways but we'll also have cycle themes and the cycle themes are the user facing enhancements that we are our goals for the cycle to deliver that way throughout the cycle even though we are using runways to focus on review priorities we still have in our heads like what user facing changes are we like working on as a whole and and help us like keep that focus throughout the cycle so they're documented here at this link and I've listed them here as well so first theme multi-cell operational enhancements we had one of the things you may have heard about is handling of down or poor performing performing cells and with cells v2 the the access pattern of of the deployment is such that the Nova API needs to talk directly to cell databases and this imposes like a lot of demand on cell databases that previously was not the case with cells v1 if you're familiar with that so to become more robust there the folks at CERN have been driving an effort to add cell resiliency functionality to the code base where if a cell is not responsive responding within a certain amount of time the cells down that will gracefully handle that and at least return like partial results or instead of just like failing to to which respond another thing we're working on is cross-cell cold migration so currently you can only migrate within a cell so works being done to be able to migrate like from one cell to another and this involves having to do things like figure out how to move the neutron ports and the volumes and all that so it's a kind of a big effort the second thing second theme we're working on improving the boot from volume experience you may be aware that people have been asking for a long time to be able to specify a volume type when creating a server and we finally added that so we're going to we're adding more robustness to boot from volume because traditionally it hasn't been like I fully supported first class feature and we're working to close those gaps another part of that is the ability to attach and detach the root volume and then volume backed server rebuild is another part of what we're working on for boot from volume and then finally the last theme is compute hosts able to upgrade and exist with nested resource providers for multiple VGP VGPU types and that may sound kind of nobulous but the basic idea here is like our current VGPU support uses a like a flat topology in placement and we're in order to support multiple VGPU types we would need to have nested resource providers on a compute host because the compute host is the root of of every the compute host is the root resource provider so we're working on being able to migrate from that flat topology to a nested one so VGP use in flat land to VGP use in nested land and then once that is done then we would be able to support multiple VGP types on a single compute host other improvements that we're working on this the cycle the placement extraction you may have heard we're we've extracted the placement code into its own repository it's going to be its own package and we've been ensuring that upgrades can can go smoothly through this upgrading from a system where placement is integrated in the Nova code base to a topology where it is a separate package and code currently the current status of that or where we're at in the in the plan is that we're implementing implementing and testing the upgrade step in triple O and open stack Ansible so the there's folks working on implementing those upgrade steps we want to make sure that the upgrade works smoothly in the major deployment tools as part of this the placement extraction another another effort we're working on this cycle bandwidth aware of scheduling so being able to express that you have network bandwidth requirements when you when you boot a server we've landed some of that code already this cycle another thing that we're looking at doing this in Stein is to move to Keystone unified limits and the Oslo limit library for enforcing quota as you may know quota limits APIs were added to Keystone semi recently and we want to move to that as the more modern way to handle quota limits and enforcement we're working on another thing we're working on is restoring the ability to set over commit per aggregate that kind of accidentally went away in in Okada when the aggregate extra or the aggregate core RAM and disc filters stopped being honored and I I sent an email about that back when it happened and we've been working to restore that ability with placement and we have a plan for that now the cycle another thing is adding configuration for the maximum number of volumes allowed to attach to a single server so you might have run into this where if you there's a limit on of 26 for the number of volumes that you can attach to a single instance using the liver driver so we're going to make that configurable so that you can set it in Nova Con per compute host to so that you can tune that for your own environment choose what number of volumes is appropriate for your environment support for emulated virtual TPM which is trusted platform module that's a blueprint that some folks are working on the cycle new more we're live migration that was we worked on that last cycle but it didn't land so we're gonna I think we're gonna work on that again the cycle try to get it done and then finally AMD seven cryptid instances so currently the memory of the virtual machines is stored in the clear and this this AMD technology for secure encrypted virtualization would allow it would it encrypts the memory of the VM so somebody's working on adding that this cycle cross project work that we're doing the cycle we were working with a sender team on a new re-image API to support the volume-backed rebuild I talked about earlier so that will that will help us do volume-backed rebuild neutron we've been working with them on the band with the worst scheduling there's we have folks that are working on that have a feature demo on Thursday if you're interested in checking that out the keystone team we've been working on with unified limits and also limit transitioning to that system and Nova there's a there's a lightning talk on Wednesday about unified limits and also limit if you're interested in learning more about how that works we've been working with the ironic team to leverage ironic conductor groups in Nova to partition Nova compute services for a group of ironic nodes cross project work continued we've been working with the Cyborg team on trying to design the Nova interaction with Cyborg so they we've been actively reviewing a spec for that you you should check that out in the know specs repository in Garrett if you're interested and there's a related presentation on Thursday about Cyborg and and everything they've been working on and then finally multiple projects we've been working on trying to work out a an approach for transfer of ownership of resources so if you've had a situation where you would like to transfer an instance from one tenant to another that's kind of that's what that's all about and it involves all the projects because there's moving neutron ports moving volumes all those sorts of things there's a forum session about that on Thursday that you should definitely attend if you're interested in that beyond Stein these are the more longer efforts that were we may not get to get to the cycle but on the radar accelerator management is going to be another you know a thing that we're going to be working on this cycle and beyond Numa modeling with placement so currently we have Numa modeling and Nova but we're not able to like combine like VGPU with Numa we we need to work on modeling Numa and placement in order to to do things like that affinity modeling and placement currently you might be aware that we have a late affinity check for dealing with races during like parallel requests for if requests for affinity and that late affinity check can't work with multi-cell and split message cues so like looking forward we really need to be able to model that in placement to handle that properly another thing that's come up more in the edge computing space is the ability to partition resources and placement this is kind of the situation where you have a shared placement service and you have say like multiple Novas talking to it and putting allocations in there currently there's no way to tell like are these allocations my Nova's allocations or are they somebody else's you're just going to get all of them if you ask for like how much VC CPUs am I using so being able to partition that is going to be required as we go forward with edge use cases and then finally a proper handling of shared storage this is an old painful one I'm sure everybody knows about we have done some of the work to handle this with placement but there's still a lot more work to do so that is definitely something we're going to be pushing for going forward so how to give feedback where we're very interactive community really want people to get involved and talk to us one of the ways you can do that is to report bugs if you experience a problem with Nova like open a bug and then ping us I if nobody's responding to your bug just ping us like come in the channel tell us about it we definitely want to want to hear from you we're very active on the on the mailing list and traditionally these have been the open-stack dev and open-stack operators mailing list but if you've seen the announcement they're going to combine all the mailing lists soon so on December 3rd they said the old the dev and the operators mailing list aren't going to be accepting posts anymore so it's going to be open-stack discuss make sure you subscribe to that before December 3rd and use the usual Nova tag and such Nova dev tag depending on what what you're hosting so how you're let us know how you're using the compute service anything that's missing any barriers to entry just come talk to us and here here's a list I've compiled of the Nova related sessions this week Souls v2 updates already happened but we've got NFV and HPC pain points tomorrow there's a session about the boot from volume improvements I talked about so if your boot from volume user that's the place to to hear what the plans are give your input make sure that's going to go and in a direction that will work for you getting operators bug fixes upstreamed I think that would be interesting for anybody that's using Nova this this discussion is going to be around like how to improve the experience for operators to connect with developers and get things fixed because I think we we could always improve there there's a session about concurrency limits for service instance creation and this is kind of about like multi-create I think and the limits around that so if you if you're running a Nova deployment where you have big bursts of like instance creates at the same time that would be an interesting session to go to and participate in as I mentioned earlier changing ownership of resources there's forum session about that where you can weigh in on the direction that that is going to go and the approach and then finally there's an update on the placement extraction from Nova that's a forum session if you're interested in learning the step more details about the status of that definitely go check that out and here's a link the at the bottom I've got a link to all the forum ether pads in case you're not aware the the forum sessions are very interactive sessions the ether pad is a place for like everybody in the room to write comments real-time ask questions make notes comments on any of the discussions going on so definitely check that out and and add your input to those ether pads how to contribute we have some contributed documentation in our docs as I mentioned earlier mailing lists very we're very active there because sometimes depending on your time zone if you come into the channel there may not be much response depending on the time if that happens send a mail to the dev list and we'll definitely see it there with the Nova tag chat with us an IRC or channels very active and don't feel intimidated I've sometimes people have told me they feel like they can't jump in because people are talking about other stuff and I just want to encourage you like just talk you know don't feel intimidated by anything in the channel and we want to hear from you want to get to know you so please chat in the channel don't feel shy we have weekly meetings in the open stack meeting channel we alternate the time to accommodate the EU time zone and the US time zone so that might be interesting to you that's that's a good place to let's say you have like a spec or a blueprint that you you'd like to get some direction on or get some eyes on you can put those in the agenda in the open discussion section that's kind of a habit that we have for people to bring to attention something they're working on that they want us to look at that we haven't looked at yet or that we whatever like if you haven't received any feedback in a while that's a good place to bring it up you can also do that in the channel at any time help with bug triage this is a big one where we very much appreciate help we have some pretty nice documentation like on how to do that but if you have any questions definitely like let us know and bug triage just means being able to take a look at it and like does this look valid how bad is this like is it really bad is it high is it low like inconvenient problem but work aroundable this is a big help to us if more people come and look at these bugs and kind of help us mark whether they're very severe or not and there's a forum session on Thursday about bug triage and how we might be able to improve that that process for everyone so that that that should be interesting and then finally we have a nova project onboarding session after lunch this is a good place to this is a kind of like small group where you can come and ask questions we're going to give you like an overview of how the architecture is and how we do things process and that's a great place to come in just ask questions and talk to us and find out like anything you're confused about about contributing just come come to that and and talk to us other ways to contribute help with code reviews this is this is always a huge help and sometimes people think like why should I review code if I'm not like a core reviewer but this actually helps a lot if you like let's say there's a bug fix that you're interested in that your organization would really like to have you review that and then just like let us know to be like I this bug fix is proposed over here and we really like we really need this and could somebody like look at this that's that's always helpful getting more people looking at the reviews and talking talking together about the ones that are interesting or critical or that's always a help to me when people let me know about interesting bug fixes that I may not have seen yet a good one that is a good way to contribute is helping to clean up the docs if you're looking at the docs and you see something that doesn't make sense or is missing like let us know better yet push a patch to fix it yourself and let us know you you've proposed the patch try to break things and report bugs we want to make sure this that Nova is working well for people so if if you found a problem please report a bug and tell us scale testing bottlenecks proposing backports yeah so if you're running an older version of Nova and you're thinking those fix landed on master and I I really like to have it in an older version you can just propose that that's totally normal there's a that I think that link is to the documentation on how the stable branch policy works so take a look at that and you definitely propose your own backwards and I think I went through that really fast but if anybody has any questions I'd be happy to try to answer them now yes I think that that falls into the affinity modeling with placement unfortunately I guess because that's going to be a big effort that's gonna be a hard problem to solve but so I would think earliest well earliest it could start we could start working on it is next cycle T but it might be even later and a lot of this is driven by like we we definitely like get a read from operators as to like what is most important so if we're seeing like this organization that organization affinity rack affinity is really the top of the list then that's kind of how we choose what to work on next so you know that kind of ties into why it's really important like to just let us know what what are the features that you most need because that's how we choose what to do first any other questions about anything contributing any of the features that I mentioned okay I guess if there's no more questions then thank you for attending and sorry I was late again


Super excited to bring my good buddy, Mr. Brandon Clay, to the stage next. Again, author, Medicare man, incredible at cross-selling, incredible at building a six-figure renewal income. Unbelievable speaker. He's one of the best speakers in the insurance industry. He really is something he's the best, you know? I'm trying to get better and level up. So maybe I can get on his level, okay? He's phenomenal, good dude, knows a ton about this industry, has been everywhere in this industry and is now a part of Heartland Financial Group in One Life America, good dude. Super excited to have him a part of it. My good buddy, come on now, bring him out to the virtual stage, Mr. Brandon Clay. You can't fail if you don't quit. My name is Brandon Clay, strategist, storyteller and coach. And I've been given the awesome opportunity and privilege by Cody Askins and the 8% Nation to address you guys in these times of challenge but also in these times of opportunity. Everything's about perception and how you see it. This country, the world, the global community has come through far greater things than this not to minimize the times we're in but this too shall pass and you can't fail if you don't quit. So I wanna take a few moments to give you my perspective on how things are right now and what you can do to actually regroup, re-engineer and redefine your life and come out stronger on the other end. So there's a few things I wanna put on your mind. Number one, don't panic. I know right now these are serious times. Look, I had the flu a little while ago, a few months ago and now I've been thinking in my mind, did I have COVID-19? But it's amazing as you're being inundated in the news and in other media outlets that this is starting to get inside of our psyche and starting to control our psychology. A few weeks ago, I literally had to say stop, no more. While I don't wanna be inundated, I wanna be informed. I wanna make sure that I govern myself in my mind because that's my greatest weapon. So as we talk about the psychology of getting through and getting to your goals and dreams, I wanna share with you three core concepts and I'll lay them out for you now. And that's to plan, that's to prepare and that's to execute. In this time where we're all sequestered, we all should be thinking about what we want in life. We should be thinking about the things we want mentally, spiritually, socially, physically and financially. We should be planning those things out almost like it was the new year because it will be a new you. First, you've got to be ready and willing to plan. Certainly now, whatever plans you had in effect may not be relevant in this current environment. So you've got to regroup, redefine and re-engineer those plans. But at the core of your objectives, it should be what you want out of life. What do you want mentally, spiritually, socially, physically and financially? The fab five is I like to call it. Don't redefine your target just because of the circumstances. You may have to redefine how you get there but don't allow the changes in the environment to make you change your core goals. So it's what you want comes first. Then it's why you want it. And these are usually emotionally based.  But as you determine your what and your why, if your why is big enough, you'll be able to endure the how. And the how becomes the strategy, the tactics, the things you're gonna do in order to reach it. In the industry I'm in, technology adoption has been compressed. What we thought might have taken 12 to 18 months for people to start engaging in is now happening at the speed of light. Why? Because people know what they want. People know why they want it. And the how has to evolve based on the circumstances. In my life, I was sharing this with Cody. When I was about his age in my mid early 20s, I tried to do some great things relative to speaking and getting out in front of people. I had booked this really large hall and I had actually sent out invitations. There was no email back then. I was on a radio show and had lots of listeners and they were all listening in. And I'd spent all the resources we had as a young couple with young kids. And when I showed up that day, the RSVPs had been fairly light and it was even worse when I turned the corner. Ultimately I had 500 empty seats with 10 people in front of me. But I engaged those 10 people like they were the most important 10 people on earth and quite candidly they were. And what I didn't know is that 30 years later that that same energy has allowed me to get in front of groups of thousands of people and speak. But my plan didn't change, my objectives didn't change, my goals didn't change. I continued to develop myself, continued to write books, continued to read books. So in this day of sequestration, you've gotta be willing to invest in self development that are targeting you and leading you toward your goals, your dreams, what you want, why you want it and how you're gonna get there. The second phase is to prepare. I talk to people all the time that are constantly getting ready which is just another form of procrastination which is usually rooted in self doubt, fear, anxiety. But I say don't get ready, be ready. There's a thing you can do today even without the perfected vehicles where you can get started on your hopes and dreams and goals for your future. You know, the Bible says put on the whole armor. It says get dressed, be equipped. Get dressed for where you wanna be. Think about the things you wanna do. Engage with people who are doing it because if it can be done and someone else is doing it and it is being done, then why not you? But you've gotta focus energy and instead of getting ready, you've got to be ready. But as you put on that whole armor and you're ready to stand, make your principled stand.  And then finally, execute. Success has a price. Achievement has a price. Are you willing to pay that price? People want excellence and success to be cheap. It's not. That's why the get rich quick scheme seem to be so prevalent and seem to be so sought after because people want it without work. People want it without labor. But there is a price to pay. And if you can pay that price just like any investment you put the seeds of capital in first. The capital is your mind, the capital is your vision, the capital is your resources. But ultimately, action is the delineator of faith. When you begin acting as if you're going to receive the thing you're seeking, then it's going to start making its appearance. Not immediately, not overnight, but in a progressive, iterative way that allows you to see the marks of progress. Look, as I think back on my own life, even as I alluded to what happened to me some 20, 30 years ago with one of my first speaking engagements that I tried to book for myself, that I realize now looking back that that was one of the greatest learning experiences I could have ever had. But it also demonstrated to me that if you don't give up, you won't fail. That you've got to keep moving and keep a inertia working on your side. We try a few things and then it fails and then we stop. But I'm telling you now that the way to build momentum is to get started and to get going. Sir Isaac Newton's Law says that an object at rest stays at rest. An object in motion stays in motion. But there's something about motion and inertia and momentum that generates an effect that ends up getting you greater and higher than you ever dream possible. So planning, preparing, execution. These are the three core tenets of my life that have allowed me to have a level of success. And look, I started out first in struggle like many of you might be right now. I worked my way to success. And then I realized that success was not enough, that I wanted to evolve into significance, that I wanted to write books and leave a legacy, which is my ultimate goal. But I wanna encourage each one of you today to dust off any dreams that you've allowed to gather dust, to get introspective in these times of quiet, in these times of solitude, in these times of isolation. If it brings you back to yourself, isolation has done a wonderful, marvelous thing. Think about all the gifts that you've been endowed with and think of how you can use them in service to mankind. I look forward to seeing all of you at the 8% nation. And until then be safe, be blessed and be successful. Thank you. A dude, is that dude eloquent with his words and one of the best public speakers, vocally that you've ever heard? Or is he one of the best? He's unbelievable. Brandon Clay, awesome job, thank you buddy. Super excited to see you do your thing and do your dance and work some magic on stage at 8% in Vegas. We're doubling down, virtual and Vegas, the two V's this year. Thank you, Brandon Clay, unbelievable job. Hey, if you love this video, stop what you're doing, click right there, I've got another phone sales videos with tips specifically for you to convert people over the phone, click on that video and I'll see you there. Today I wanna talk about five easy phone sales tips that you can implement right away and see success with, okay? So stay with me as I go through each one of these, all right?


Now I'm going to quickly jump into the actual operations on vectors, operations on vectors, fine. So operation on vectors we'll first talk about addition, addition of vectors and I think you have done this a couple of times to find resultant that's why we call it as finding the resultant of vectors also, okay? Addition is as good as finding the resultant of vectors. So when you add two vectors A and B and you get a vector C from it, we call C as the resultant of A and B. Now how do we add two vectors? There are multiple ways to do it. The first way that we are going to talk about is the parallelogram law of addition. So first method is a parallelogram law of addition. Suitable for those cases where your vector is localized, okay? But it can also be applied to free vectors, okay? So parallelogram law of addition is used when your vectors are localized. For example, if you want to, if there's a, if there are multiple forces acting on a body, that's it is a body of mass M and force F1 is acting in this way, force F2 is acting in this way and you want to find out the resultant of these two forces, okay? Then we can use the parallelogram law of addition. This law says that if you have two vectors, let's say vector A is like this and vector B is like this. Let me draw it slightly. Yeah. If you want to add them or if you want to find the resultant of these two vectors, first make them co-initial, okay? How do you make them co-initial? By connecting their initial points. So this is the initial point of A. This is the initial point of B. Let me make it co-initial. So if you make it co-initial, you have to either take A parallel to itself so that it comes over here or take B parallel to itself so that it comes over here, okay? Any of the two you can do. So let's say I take B vector parallel to itself. So A is like this. B, I brought it like this, okay? Remember I have not changed their magnitude and direction. So this law says that complete a parallelogram, complete a parallelogram such that these two vectors form the adjacent sites of the parallelogram. Once you have completed the parallelogram, a vector originating from the common co-initial point going till this opposite end, that vector would be called your resultant of A and B, okay? Couple of things here to be noted that this A plus B will always be having a magnitude less than equal to the sum of the individual magnitudes of A and B, okay? This is because of the triangle being formed over here. So as you can see, this is your vector A, okay? So if you see this triangle, A plus B is magnitude of A plus B is the length of the third site which will always be less than the sum of the other two sites, okay? This is also called the triangle inequality, okay? Next method that we normally adopt to add vectors is called the triangle law or triangular law of addition, okay? In this, what do we do is we connect the terminal point of one with the initial point of the other. So let me take the same two cases. This is your vector A and this is your vector B, okay? So what do we do? We connect the terminal point of A to the initial point of B. You can do the other way around also. It doesn't make a difference. You can connect the terminal point of B with the initial point of A. So let me do that. So let's say A goes like this, B is like this, okay? B is like this. Then a vector starting from the initial point of A and going to the terminal point of B, that vector would be your A plus B vector. That means you're completing a triangle by doing this, okay? That's why it is called the triangular law of addition of vectors, okay? And same inequality holds true in this case as well. Now triangular law of addition is actually a very specific case of what we call as the polygon law of addition. Polygon law of addition is suitable for those cases where you have more than two vectors involved, okay? More than two vectors involved, okay? For example, if I have a vector like this A, any other vector B, and other vector like this C, okay? If I want to add these vectors, what I do is, again, I start connecting the terminal of one with the initial of the other, terminal of one with the initial of the other. And this you can do it in any order. It doesn't have to start from A. You can start with B also. You can start with C also. But just keep connecting the terminal of one with the initial of the other. For that, you need to move these vectors around also. So let's say I connect A, then I connect B, then I connect C. Let's say C, okay? So triangular polygon law says that the resultant would be a vector connecting the initial point of the first vector to the terminal point of the last vector. And normally in your books and all, they would draw this with dotted lines, okay? This line represents that this is the resultant of all these, okay? So this vector will be your A plus B plus C, okay? Couple of properties that we need to know about vector addition, properties of vector addition. First property is vector addition is commutative. It doesn't matter whether you're doing A plus B or B plus A. They are commutative. Secondly, they are associative. So it doesn't matter whether you add A plus B and then add the resultant to C or whether you add A to the resultant of B and C, okay? So this is associative. Third, zero vector is called the identity vector, okay? So zero is called here. Zero is the additive identity. These terms have actually evolved because vectors form a very important vertical under linear algebra, okay? So you need to know this however there's no direct uses of it. Then there's something called additive inverse. So my negative of a vector is called its additive inverse. So we say my negative A is the additive inverse, additive inverse of vector A, okay? And I've already told you the triangle inequality that is A plus B mod will always be less than equal to mod A plus mod B. Equality will hold true when your A and B are in the same direction, okay? Equality will hold when your A and B will be in the same direction. Okay? Now when we talk about subtraction of vectors, we don't have to deal separately with subtraction of vectors because subtraction is actually covered under addition of A with negative of B. Now what is negative of B? Negative of any vector is nothing but it's a vector with the same magnitude. Let's say negative of a vector, let's say I call it the vector as vector P, okay? Negative of a vector P is a vector which is having the same magnitude as P but direction is reversed. But the direction of, but the direction is reverse of P, okay? I'm going to talk more about it in the scalar multiplication. The direction is reverse of P, okay? For example, if I say vector A is going 10 kilometers towards north, then negative A is nothing but going 10 kilometers towards south, okay? Simple as that. So when you are subtracting two vectors, you are adding A with the negative of B, okay? So let's say these are my vectors A, okay? And this is my vector B. I want to find A minus B. I want to find A minus B. So what do I do is first of all, I reverse the direction of this vector. So that means let me take the reverse of vector B which is like this. Then I can follow any of the two laws that we have seen whether triangle law of addition or parallelogram law of addition doesn't matter. So let's say I follow the parallelogram law of addition. So first I have to make them co-initial, okay? So this is the initial point of A. This is the initial point of B minus B. So I have to make them co-initial. So let me do it like this, okay? This is my A and this is my minus B. Then I complete a parallelogram like this, okay? This vector here would be your A minus B vector, okay? Now let me show you something very interesting. Had you completed a parallelogram with A and B itself, let's say I complete a parallelogram with A and B itself, okay? Of course this diagonal will represent A plus B, okay? This is your A plus B vector, okay? And you would be happy to know that in the same parallelogram, had you connected the other diagonal, as you can see this length and this length are exactly the same. Now the direction has to be from the B point towards the A vector here. This vector will now represent a A minus B vector. So in the same parallelogram, one of the diagonal represents A plus B, other diagonal represents A minus B, okay? Now I'm going to begin with something which is very important for problem solving position vectors, okay? What are position vectors? First of all, before I talk about them, let me tell you these are the concepts which are going to connect vectors, which are going to relate vectors to coordinate geometry. That's why it becomes very important that we understand this concept of position vector very, very carefully because many of the geometrical theorems or proofs can be done through vectors if we are able to understand what is position vector, okay? Now what is position vector? Position vector is a vector which connects the position of a point with a reference position, okay? With a reference position, which we normally call as the zero vector also or the origin. So what is origin in case of coordinate geometry is the reference point or reference vector in case of vectors. So a vector which connects O to P like this, this vector would be called as the position vector. This vector would be called as the position vector of P, position vector of P, okay? And normally we write it like this. Let's say I call it as vector P. So this is your P vector, okay? Now let me tell you this is a very, very, I would say rare way of representing a point's position vector. Normally they just say P having a position vector of this. They will never show you the origin, okay? Origin is up to you to choose. See it's just like mentioning a point. Let's say I say there's a point 1, 2. Do I tell you that where is the origin? No, right? You choose your origin and accordingly you make a point 1, 2. So origin position is never specified. It is up to you to choose your origin position, correct? Wherever you choose the origin position, relative to that you choose 1, 2, correct? In the same way if I say the position vector of a point is let's say P vector, I would never say where is my origin. It is up to you to choose what is the position of the origin, okay? I will just specify something like this. P has a position vector of P, okay? So I will say something like this. P has a position vector of P, Q has a position vector of Q, okay? Now let me ask this as a question. What will be P Q vector then? Can somebody tell me what is P Q vector in terms of small p and small q? Sir, are you asking the distance between p and q? No, no, I'm talking about the vector p and q. Come on, I think you've done this chapter in school, right? Okay, I've got some response. Q minus p, Shia says Q minus p. Why not P minus q? How do you know it's Q minus p? Sir, they have the same initial point origin so we need to take minus p in order to do it. Okay, see let's say I take the origin over here, okay? Now it's up to me where I take this origin, okay? So when I say position vector of P is P, what does it mean? It means that a vector connecting, a vector connecting O to P is this P vector, correct? A vector connecting O to Q is your Q vector, correct? Yeah. Now if you want to think as if you want to travel from P to Q, okay? And the only roads available are this road and this road. See the motion of my cursor. You can only take the known roads, this road and this road, correct? So if you want to go from or you can use your vector addition, see vector addition is nothing but trying to figure out alternative way to accomplish that vector path, okay? So what I normally tell people who have not been introduced to vector addition is that let's say you're trying to go from P to Q. So I'll take the path from P to O first, okay? Now when you're going from P to O you are traveling minus P vector, correct? Because you're going in the reverse direction of P. Now you're going from O to Q. O to Q means you're going in the direction of Q. So basically this will become Q minus P as you rightly said, okay?   So P plus let's say P Q is a known vector. This will be equal to Q. So from here also we end up getting the same answer. Now in order to facilitate remembering of this normally I say if you want to go from A to B it's nothing but position vector of B minus position vector of A. Just remember this formula, okay? I call this as destination minus source. So wherever you're going that is your destination. From where you're coming that is your source. So A B is nothing but destination minus the source position vector. Okay? Now if this concept is clear we'll take few problems on this but before that I would like you to solve a simple question. Let's say this is a regular hexagon A B C D E F, okay? Let's say A B vector is A, B C vector is B, okay? Find the following vectors in terms of A and B. One is C D vector. So tell me what is C D vector, D vector, E F vector and F A vector. In terms of A and B express these following vectors. Remember it's a regular hexagon. I'm sure at least D vector and E F vector you can say very easily, correct? Yes. What is that? D will be minus A. Correct. D it is minus A. E F will be? Minus B. C D if you can find out the negative of C D will be F A, right? But how do you find C D? Sir can we say that the sum of this whole thing will be like zero? So it doesn't help you because C D and minus F A will cancel, A B and D will be cancelling, B C and E F will be cancelling. So how does it end up giving you the value of C D and E F? Yes. Any idea? Okay let me help you out. Would you all agree with me that this vector here would be 2B vector because this is in the same direction of B and double of the vector B because of geometry. Okay should I show you how it is double the length? I'm sure you can figure it out. This is 60 degree correct. So this will be let's say this length, whatever is this length, X. This will be X by 2. Similarly here also it will be X by 2. Okay and this is X itself. So X, X by 2, X by 2 will make it to X length. Okay so since the direction is the same and the magnitude is double of that of B, I can call this vector as 2B. Correct? Now let us use the polygon law of addition. So can I say A B plus B C plus C D will be equal to A D. A B plus B C plus C D is equal to A D. A B is A. B C is B. C D not known to me but A D is 2B. So can I say C D vector will be nothing but take it on the other side will become B minus A. So C D is B minus A. So F A would automatically be A minus B. Clear?