SOLUTION: Consider only vectors in R^3 Please help with this PROOF if u dot v = u dot w for all u, then v = w not using a counterexample... thanks for your help

Algebra ->  Proofs -> SOLUTION: Consider only vectors in R^3 Please help with this PROOF if u dot v = u dot w for all u, then v = w not using a counterexample... thanks for your help      Log On


   

Question 436451: Consider only vectors in R^3
Please help with this PROOF
if u dot v = u dot w for all u, then v = w
not using a counterexample... thanks for your help
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
u%2Av+=+u%2Aw for all u
==> u%2Av+-+u%2Aw+=+u%2A%28v-w%29+=+0, for all u.
From a previous problem you posted I showed that, if u*z = 0 for all u, then z is equal to the zero vector. Then, from this should follow that v - w = 0, or v = w.