Question

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

Answer 1

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 + 2AB Cos theta`

Thus we get,
`C = [A^2 + B^2 +2AB Cos theta]^(1/2)`

This, is the law of cosines.