Chapter 5 - Inner Product Spaces - 5.2 Orthogonal Sets of Vectors and Orthogonal Projections - True-False Review - Page 359: f

True

$u$ and $v$ are orthogonal vectors and $w$ is any vector We have the notation for the inner product: $P(w,v)=\frac{}{||v||^2}v$ then $P(P(w,v),u)=\frac{P}{||u||^2}u=\frac{||v||^2}{||u||^2}u=\frac{}{||v||^2}.\frac{}{||v||^2}u$ Since $u$ and $v$ are orthogonal vectors we have $=0 \rightarrow P(P(w,v),u)=0$