Prove that if ||u||=||v||, then (u+v)·(u−v) = 0.

beljuA 2021-01-08 Answered
Prove that if ||u||=||v||,then(u+v)·(uv)=0.
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Expert Answer

StrycharzT
Answered 2021-01-09 Author has 102 answers
Suppose u,v are two vectors in a real inner product space V such that u∥=∥v. Then, from the properties of the inner product (i.e. dot product), we see that
(u+v)×(uv)=u×uu×v+v×uv×v=(u2)u×v+u×v(v2)=(u2)(v2)=(v2)(v2)=0
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