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Finding Magnitude of Vector

  1. Jan 28, 2012 #1
    1. The problem statement, all variables and given/known data
    Let u = <3,-1>. Find v such that ||v||=4 and the angle between the vectors is ∏/3.


    2. Relevant equations

    u.v = ||u|| ||v|| cos θ

    3. The attempt at a solution

    <3,-1>.v = (√10)(4) cos ∏/3
    <3,-1>.v = 2√10
    v = <(2√10)/3, (2√10)/-1>

    Can you please confirm that I am doing this correctly, or if not help me through where I am going awry?
     
  2. jcsd
  3. Jan 28, 2012 #2

    SammyS

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    You're not doing this correctly. The v you have has a magnitude that's way too big.

    Write vector, v, as v = <vx, vy>, where vx2 + vy2 = 16 .
    Solve this for vy.​

    Your lines:
    <3,-1>∙v = (√10)(4) cos ∏/3

    <3,-1>∙v = 2√10​
    are fine.

    But in the next line, it looks like you tried to divide by the vector <3,-1>. There is no such thing as vector division !

    Compute <3,-1>∙v = (3)vx + (-1)vy.

    Of course that gives you: (3)vx + (-1)vy = 2√(10)

    Solve that equation and the equation, vx2 + vy2 = 16, simultaneously.
     
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