SOLUTION: Consider only vectors in R^3 Proof: if v dot w = 0 for all v, then w = 0 Please help, i tried through a counterexample and my professor didn't like it.

Algebra ->  Proofs -> SOLUTION: Consider only vectors in R^3 Proof: if v dot w = 0 for all v, then w = 0 Please help, i tried through a counterexample and my professor didn't like it.      Log On


   

Question 436449: Consider only vectors in R^3
Proof: if v dot w = 0 for all v, then w = 0
Please help, i tried through a counterexample and my professor didn't like it.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
It follows from the hypothesis that w%2Aw+=+abs%28w%29%5E2+=+0 ==> abs%28w%29+=+0. Only one vector has 0 magnitude, and that is the zero vector. Hence w is the zero vector.