- The plane \(P\) has equation
$$\mathbf { r } = \left( \begin{array} { l }
3
1
2
\end{array} \right) + \lambda \left( \begin{array} { r }
0
2
- 1
\end{array} \right) + \mu \left( \begin{array} { l }
3
2
2
\end{array} \right)$$
- Find a vector perpendicular to the plane \(P\).
The line \(l\) passes through the point \(A ( 1,3,3 )\) and meets \(P\) at \(( 3,1,2 )\).
The acute angle between the plane \(P\) and the line \(l\) is \(\alpha\).
- Find \(\alpha\) to the nearest degree.
- Find the perpendicular distance from \(A\) to the plane \(P\).