Question

In a triangle ABC, using vectors, prove that c² = a² + b² – 2ab cos c.

Answer 1

`veca + vecb + vecc = vec0`

`veca + vecb = -vecc`

Squaring on both sides, we have

`(veca + vecb) (veca + vecb) = (-vecc) (-vecc)`

`b^2 + a^2 + 2ab cos  ( π - c) = c^2`

`b^2 + a^2 + 2ab   ( - cos c ) = c^2`

`c^2 = a^2 + b^2 - 2ab  cos  c`