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Vectors and Trigonometry

  1. Jan 22, 2009 #1
    A screenshot of the problem:

    2. Relevant equations
    Not sure... possibly the dot product of two vectors?

    v*w = a(1)a(2) + b(1)b(2)

    3. The attempt at a solution
    Part of the problem is that I'm not entirely sure what the question is asking for. I think it's talking about the coefficents for the two vectors which will allow those vectors to produce the same vector as X.

    I tried plugging (2*pi/5) into the equations above and adding them together giving me (using decimal approximations because I don't know how to find the exact values):

    U + V = -.642 I + 1.260 J

    Then I try replacing X for:

    8I + 3J = -.642 I + 1.260 J

    Which doesn't make much sense to me... should I treat I and J as variables and solve for them? I think I'm on the completely wrong track.
  2. jcsd
  3. Jan 22, 2009 #2
    By dumb luck, it appears that you have found that u=1 and v=1 is the solution to your problem. Now you need to go back to find that in some rational manner, rather than simply guessing at the answer.

    How about starting by writing
    X = u U + v V and then taking a dot product with U? What will that get you?
  4. Jan 22, 2009 #3
    heh, well the problem is that isn't the right answer (it's an online submission process, and apparently 1 is not the correct answer)

    Going from another angle, I thought about trying to reduce it to two equations of two variables... something like:


    where a = theta.

    If I do that, though, how do I find exact values for sin(2pi/5) and cos(2pi/5)?
  5. Jan 22, 2009 #4
    If you do as I suggested, and write
    X = u U + v V = 8I + 3J
    X.U = u = (8I + 3J).(cos theta I + sin theta J) = 8 cos theta + 3 sin theta
    which you can then evaluate. Does that do anything for you?
  6. Jan 22, 2009 #5
    Ah, actually yeah.

    solving all the way through

    u ~ 5.325
    v ~ -6.682


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