3 The line \(l _ { 1 }\) has equation \(\mathbf { r } = \left( \begin{array} { r } 1
- 3
3 \end{array} \right) + \lambda \left( \begin{array} { r } 3
2
- 2 \end{array} \right)\).
The plane \(\Pi\) has equation \(\mathbf { r } \cdot \left( \begin{array} { r } 2
- 5
- 3 \end{array} \right) = 4\).
- Find the position vector of the point of intersection of \(l _ { 1 }\) and \(\Pi\).
- Find the acute angle between \(l _ { 1 }\) and \(\Pi\).
\(A\) is the point on \(l _ { 1 }\) where \(\lambda = 1\).
\(l _ { 2 }\) is the line with the following properties.
- \(l _ { 2 }\) passes through \(A\)
- \(l _ { 2 }\) is perpendicular to \(l _ { 1 }\)
- \(l _ { 2 }\) is parallel to \(\Pi\)
- Find, in vector form, the equation of \(l _ { 2 }\).