Problem

The plane $\Pi$ has equation

$$\mathbf r=\begin{pmatrix}1\\2\\3\end{pmatrix} +\lambda\begin{pmatrix}0\\3\\-2\end{pmatrix} +\mu\begin{pmatrix}1\\1\\2\end{pmatrix}$$

where $\lambda$ and $\mu$ are scalar parameters.

(a) Determine a vector perpendicular to $\Pi$

The line $l$ meets $\Pi$ at the point $(1,2,3)$ and passes through the point $(1,0,1)$

(b) Determine the size of the acute angle between $\Pi$ and $l$

Give your answer to the nearest degree.

(c) Determine the shortest distance between $\Pi$ and the point $(6,-3,-6)$