# How can vector dot products be used to prove the law of cosines?

May 30, 2015

That's very simple, I'll show you how,
Let,
A + B = C

Thus, one may write,
C. C = (A + B).(A + B)
this implies, that
${C}^{2} = {A}^{2} + {B}^{2} + 2 A B C o s \theta$

Thus we get,
$C = {\left[{A}^{2} + {B}^{2} + 2 A B C o s \theta\right]}^{\frac{1}{2}}$

This, is the law of cosines.