Question

If u, v and w are non-zero vectors such that u • (v + w) = v • (u − w), show that w is perpendicular to (u + v). Show all steps.

Answer 1

since the dot product is associative and commutative, we have
u•v + u•w = u•v - v•w
u•w + v•w = 0
(u+v)•w = 0
so they are perpendicular