Chapter 11 - Vectors and the Geometry of Space - 11.4 Exercises - Page 782: 50

TRUE.

Assume that $$ v-w \neq 0 $$ $ u.v =u.w$ $\rightarrow$ $u.(v-w)=0$, which means $u$ and $v-w$ are perpendicular to each other. $u\times v=u\times w$ $\rightarrow$ $u\times{(v-w)}=0$, which means $u$ and $v-w$ are parallel to each other. But two vectors can not be parallel as well as perpendicular to one another Thus, we have$$ v-w=0 \rightarrow v=w.$$