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Need help solving for unknown components

  1. Jan 24, 2009 #1
    1. The problem statement, all variables and given/known data
    Vector A = (2x-y)m and Vector B= (x+ay)m (a is alpha, m is meters)

    If |A+B|=5m, determine the possible values of a.


    2. Relevant equations

    The magnitude of A= sqrt 5

    3. The attempt at a solution

    |A^2 + B^2|=5^2
    |(2x-y)^2 + (x+ay)^2|= 5^2
    |(2x-y)^2 + (x+ay)^2|= 25

    I cannot figure out how to solve this problem. Please help!
     
  2. jcsd
  3. Jan 24, 2009 #2

    rl.bhat

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    Vector A = (2x-y)m and Vector B= (x+ay)m (a is alpha, m is meters)

    This statement is not clear. Here what is x and y? Are they equivalent i and j?
    If that is the case, find cos(theta) between A and B using dot product. Use this cos(theta) in R^2 = A^2 + B^2 +2AB*cos(theta) to get values of alpha.
     
  4. Jan 24, 2009 #3
    I'm a little confused by your notation, do you mean:

    A = <2, -1>; B = <1, a>?

    If so add the vectors then take the magnitude and solve for a it should get you a quadratic, I think.
     
  5. Jan 24, 2009 #4
    yes thats what i mean. What would be the result of adding those? That's where im stuck
     
  6. Jan 24, 2009 #5

    rl.bhat

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    Then follow the post 2.Or
    R^2 = A^2 + B^2 +2A.B and solve for alpha
     
    Last edited: Jan 24, 2009
  7. Jan 24, 2009 #6
    what do you get when you square B?
     
  8. Jan 24, 2009 #7
    A+B = <3, (a-1)>

    [tex]|A+B| = \sqrt{9 + (a-1)^2} = 5[/tex]

    Just solve for a...
     
  9. Jan 24, 2009 #8

    rl.bhat

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    1 + a^2
     
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