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

[ARJewell]

Homework Statement

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

Homework 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

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?

 

[Filip Larsen]

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.