2 The lines \(L _ { 1 }\) and \(L _ { 2 }\) have the following equations.
\(L _ { 1 } : \mathbf { r } = \left( \begin{array} { c } - 5
6
15 \end{array} \right) + \lambda \left( \begin{array} { c } 5
- 2
- 2 \end{array} \right)\)
\(L _ { 2 } : \mathbf { r } = \left( \begin{array} { c } 24
1
- 5 \end{array} \right) + \mu \left( \begin{array} { c } 3
1
- 4 \end{array} \right)\)

1. Show that \(L _ { 1 }\) and \(L _ { 2 }\) intersect, giving the position vector of the point of intersection.
2. Find the equation of the line which intersects \(L _ { 1 }\) and \(L _ { 2 }\) and is perpendicular to both. Give your answer in cartesian form.