Problem

The plane $\Pi$ has equation

$$\mathbf{r} = \begin{pmatrix} -1 \\ 5 \\ 2 \end{pmatrix} + \lambda \begin{pmatrix} 2 \\ 0 \\ 7 \end{pmatrix} + \mu \begin{pmatrix} 3 \\ -2 \\ 3 \end{pmatrix}$$

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

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

The line $l$ passes through the point $A(1, 7, 3)$ and meets $\Pi$ at the point $B(-1, 5, 2)$ The acute angle between $\Pi$ and $l$ is $\alpha$

(b) Determine the value of $\alpha$ to the nearest degree.

(c) Determine the exact shortest distance from A to $\Pi$