7 The lines \(l _ { 1 }\) and \(l _ { 2 }\) have equations
$$\begin{aligned}
& l _ { 1 } : \mathbf { r } = \left[ \begin{array} { c }
3
1
- 2
\end{array} \right] + \lambda \left[ \begin{array} { c }
3
- 4
1
\end{array} \right]
& l _ { 2 } : \mathbf { r } = \left[ \begin{array} { c }
- 12
a
- 3
\end{array} \right] + \mu \left[ \begin{array} { c }
3
2
- 1
\end{array} \right]
\end{aligned}$$
7
- Show that the point \(P ( - 3,9 , - 4 )\) lies on \(l _ { 1 }\)
7 - Show that \(l _ { 1 }\) is perpendicular to \(l _ { 2 }\)
7 - Given that the lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect, calculate the value of the constant \(a\)
7
- Hence, find the coordinates of the point of intersection of \(l _ { 1 }\) and \(l _ { 2 }\)