- The plane \(\Pi\) has equation
$$\mathbf { r } = \left( \begin{array} { l }
1
2
3
\end{array} \right) + \lambda \left( \begin{array} { r }
0
3
- 2
\end{array} \right) + \mu \left( \begin{array} { l }
1
1
2
\end{array} \right)$$
where \(\lambda\) and \(\mu\) are scalar parameters.
- Determine a vector perpendicular to \(\Pi\)
The line \(l\) meets \(\Pi\) at the point ( \(1,2,3\) ) and passes through the point ( \(1,0,1\) )
- Determine the size of the acute angle between \(\Pi\) and \(l\)
Give your answer to the nearest degree.
- Determine the shortest distance between \(\Pi\) and the point \(( 6 , - 3 , - 6 )\)