# 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 ->  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

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 Logic: Proofs Solvers Lessons Answers archive Quiz In Depth

 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(4012)   (Show Source): You can put this solution on YOUR website!It follows from the hypothesis that ==> . Only one vector has 0 magnitude, and that is the zero vector. Hence w is the zero vector.