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Proof of Cosine law using vectors

  1. Mar 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Two vectors of lengths a and b make an angle θ with each other when placed tail to tail. Prove, by taking components along two perpendicular axes, that the length of the resultant vector is r=√(a^2+b^2+2abcos θ )

    2. Relevant equations

    Would this be correct?
    How would you simplify it?:uhh:

    3. The attempt at a solution
    So ax = acos θ , bx = bcos θ , ay = asin θ , by = bsin θ. So rx = ax + bx and ry = ay + by . So r=√(r_x+r_y ) .
    Which means that, √(〖[(a+b)cosθ]〗^2+〖[(a+b)sinθ]〗^2 )
  2. jcsd
  3. Mar 20, 2009 #2


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    Homework Helper

    Let vector a be along x-axis and vector b makes an angle theta with x-axis.
    Now take the component of b along x and y axis. Find net x component and y component and find the resultant.
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