6 The line \(l _ { 1 }\) passes through the point \(A ( 0,6,9 )\) and the point \(B ( 4 , - 6 , - 11 )\).
The line \(l _ { 2 }\) has equation \(\mathbf { r } = \left[ \begin{array} { r } - 1
5
- 2 \end{array} \right] + \lambda \left[ \begin{array} { r } 3
- 5
1 \end{array} \right]\).

1. The acute angle between the lines \(l _ { 1 }\) and \(l _ { 2 }\) is \(\theta\). Find the value of \(\cos \theta\) as a fraction in its lowest terms.
2. Show that the lines \(l _ { 1 }\) and \(l _ { 2 }\) intersect and find the coordinates of the point of intersection.
3. The points \(C\) and \(D\) lie on line \(l _ { 2 }\) such that \(A C B D\) is a parallelogram.
   \includegraphics[max width=\textwidth, alt={}, center]{c42685e9-bfa4-48d4-8abb-13e88a4b765e-12_392_949_1018_548} The length of \(A B\) is three times the length of \(C D\).
   Find the coordinates of the points \(C\) and \(D\).
   [0pt] [5 marks] \(7 \quad\) A curve \(C\) is defined by the parametric equations $$x = \frac { 4 - \mathrm { e } ^ { 2 - 6 t } } { 4 } , \quad y = \frac { \mathrm { e } ^ { 3 t } } { 3 t } , \quad t \neq 0$$