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3D Vectors and resultant force

  1. Nov 17, 2013 #1

    The vertices of a quadrilateral are A(1,2,-1) B(-3,2,-3) C(4,1,-4) and D(2,-1,3). At A forces of magnitude 4, 5 and 4 are newtons act along AB, AC, and AD respectively. Find the resultant force.

    Looking for more of a hint than an answer.

    Any help would be appreciated x
  2. jcsd
  3. Nov 17, 2013 #2
    The problem essentially gave you the direction of three forces, and their magnitudes. From these you could write the three forces as vectors, [itex]\vec{F_1}[/itex], and then add the vectors to give you the direction and magnitude of the resultant net force
  4. Nov 17, 2013 #3


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    Welcome to PF!

    Hi Skittlz! Welcome to PF! :wink:

    Start by writing out the three vectors …

    show us what you get. :smile:
  5. Nov 17, 2013 #4
    By adding I get AB = (-2,4,-4) AC = (5,3,-5) and AD = (3,1,2) would I then add these 3 vectors to get the direction and then use Pythagoras to find the magnitude?

    Edit: this is wrong.
    Last edited: Nov 17, 2013
  6. Nov 17, 2013 #5


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    Hi Skittlz! :smile:
    No, for the vector joining A and B, you need to subtract, (not add) …

    the vector AB is OB - OA (where O is the origin), ie the coordinates of B minus the coordinates of A. :wink:
    Yes. :smile:

    (but you will stil need to use moments, to find the correct line of application, or at least any point on that line)
  7. Nov 17, 2013 #6
    I see, thanks!

    One thing I still don't understand. what am I supposed to do with the given forces?
  8. Nov 17, 2013 #7


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    eg the force along AB is of magnitude 4 …

    the vector AB (found by subtraction) tells you the direction, and you then have to multiply that by something (it isn't 4 ! :wink:) to get the actual force …

    show us what you get :smile:
  9. Nov 17, 2013 #8
    I know not to multiply by 4 as that just makes the vector larger i.e 4 times larger in this case. But 4N is the force across the vector which would mean |AB| = 4 right? So given that AB = (4,0,2) - (by subtracting) the magnitude would be srt20 right? but we are told that it is 4 so do we multiply by arbitrary values of x,y,z so that srt(4x^2+0y^2+2z^2) = 4 ? or is this wrong?

    I feel like I'm missing something quite important here but not sure what - vectors are a very big problem for me :(
  10. Nov 17, 2013 #9


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    HiSkittlz! :smile:

    Think in terms of unit vectors.
    Right :smile:

    So the unit vector along AB is (4/√20, 0 2/√20) …

    that's what you multiply by 4 ! :wink:
  11. Nov 17, 2013 #10
    Ah I see now, so what i do is:

    Find each unit vector then multiply by the force across it e.g.

    unit vector of AB = 4 x (4/√20, 0, 2/√20)

    Then do the same for the other two and then add the forces to find the resultant force.
  12. Nov 17, 2013 #11


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    yup! :biggrin:

    (and use moments to find the line of application)
  13. Nov 17, 2013 #12
    Thanks for the help :D

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