Hello PF! 1. The problem statement, all variables and given/known data Prove the following: if u and v are two vectors in Rn such that u[itex]\cdot[/itex]w = v[itex]\cdot[/itex]w for all wεRn , then we have u = v 2. Relevant equations 3. The attempt at a solution u[itex]\cdot[/itex]w - v[itex]\cdot[/itex]w = 0 w[itex]\cdot[/itex](u - v) = 0 I'm not sure what to do after applying the distributive property (in reverse). How do I go about proving that the vectors u and v are equal? I considered establishing two cases in which w = 0 and u-v = 0 but that doesn't help me out. Are there any properties that I can use to construct this proof?