Exercise 1

Project the first vector orthogonally into the line spanned by the second vector.

• (a)  $\begin{pmatrix}2\\ 1\end{pmatrix}$, $\begin{pmatrix}3\\ -2\end{pmatrix}$     (b)  $\begin{pmatrix}2\\ 1\end{pmatrix}$, $\begin{pmatrix}3\\ 0\end{pmatrix}$     (c)  $\begin{pmatrix}1\\ 1\\ 4\end{pmatrix}$, $\begin{pmatrix}1\\ 2\\ -1\end{pmatrix}$     (d)  $\begin{pmatrix}1\\ 1\\ 4\end{pmatrix}$, $\begin{pmatrix}3\\ 3\\ 12\end{pmatrix}$