Exercise 5

Suppose that $\wvec=\threevec2{-1}2$ defines a line $L$ in $\real^3$.

1. Find the orthogonal projections of the vectors $\threevec100$, $\threevec010$, $\threevec001$ onto $L$.

2. Find the matrix $P = \frac{1}{\len{\wvec}^2} \wvec \wvec^T$.

3. Use this proposition to explain why the columns of $P$ are related to the orthogonal projections you found in the first part of this exercise.