WeBWorK Standalone Renderer

For each of the following pairs of vectors $\mathbf{x}$ and $\mathbf{y}$ , find the vector projection $\mathbf{p}$ of $\mathbf{x}$ onto $\mathbf{y}$ .

(a) $\mathbf{x} = \left[\begin{array}{c} -3 \\ 1 \\ -3\end{array} \right]$ and $\mathbf{y} = \left[\begin{array}{c} 2 \\ -1 \\ 1\end{array} \right]$

$\mathbf{p} =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$		$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

(b) $\mathbf{x} = \left[\begin{array}{c} \sin(t) \\ \cos(t) \\ 1\end{array} \right]$ and $\mathbf{y} = \left[\begin{array}{c} \cos(t) \\ -\sin(t) \\ 3\end{array} \right]$ where $t$ is some angle.

$\mathbf{p} =$

$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right[$		$\left.\vphantom{\begin{array}{c}\!\strut\\\!\strut\\\!\strut\\\!\strut\\\end{array}}\right]$

You can earn partial credit on this problem.