7 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations \(\mathbf { r } = \left[ \begin{array} { r } 8
6
- 9 \end{array} \right] + \lambda \left[ \begin{array} { r } 3
- 3
- 1 \end{array} \right]\) and \(\mathbf { r } = \left[ \begin{array} { r } - 4
0
11 \end{array} \right] + \mu \left[ \begin{array} { r } 1
2
- 3 \end{array} \right]\) respectively.

1. Show that \(l _ { 1 }\) and \(l _ { 2 }\) are perpendicular.
2. Show that \(l _ { 1 }\) and \(l _ { 2 }\) intersect and find the coordinates of the point of intersection, \(P\).
3. The point \(A ( - 4,0,11 )\) lies on \(l _ { 2 }\). The point \(B\) on \(l _ { 1 }\) is such that \(A P = B P\). Find the length of \(A B\).