Question 436451
{{{u*v = u*w}}} for all u
==> {{{u*v - u*w = u*(v-w) = 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.