Asked by big123
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.
Answers
Answered by
oobleck
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
u•v + u•w = u•v - v•w
u•w + v•w = 0
(u+v)•w = 0
so they are perpendicular
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