Question

show that if u dot v = u dot w for all u, then v = w.

You can use the result of the previous problem:

http://www.jiskha.com/display.cgi?id=1184622247

Linearity of the inner product implies

u dot v = u dot w ----->

u dot(v-w) = 0

This is true for all u, therefore the result of the previous problem says that:

v - w = 0 ---->

v = w