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How to Prove that A*B= |A||B|cos theta

  1. Apr 11, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that A*B = |A||B|cos theta


    2. Relevant equations
    Law of cosines: c^2= a^2 + b^2 - 2abcostheta
    Property of a dot product; x*x=x^2
    Replace c^2, a^2, and b^2 with dot product
    3. The attempt at a solution

    c*c=a*a+b*b-2abcostheta
    since c=a-b
    c*c= (a-b) * (a-b)
    c*c= (a*a-2a*b+b*b)

    therefore
    (a*a-2a*b+b*b) = a*a+b*b-2abcostheta
    -2a*b=-2abcostheta
    a*b=abcostheta


    Does this look right?
     
  2. jcsd
  3. Apr 12, 2010 #2

    Filip Larsen

    User Avatar
    Gold Member

    It looks right to me. If you need to refer to all the rules you apply in each step of your proof, you should probably notice that you utilized that the inner product is commutative and distributive.
     
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