3．The lines \(L _ { 1 }\) and \(L _ { 2 }\) have the equations $$L _ { 1 } : \mathbf { r } = \left( \begin{array} { l } 1
0
9 \end{array} \right) + s \left( \begin{array} { l } 2
p
6 \end{array} \right) \quad \text { and } \quad L _ { 2 } : \mathbf { r } = \left( \begin{array} { r } - 15
12
- 9 \end{array} \right) + t \left( \begin{array} { r } 4
- 5
2 \end{array} \right)$$ where \(p\) is a constant．
The acute angle between \(L _ { 1 }\) and \(L _ { 2 }\) is \(\theta\) where \(\cos \theta = \frac { \sqrt { 5 } } { 3 }\)
（a）Find the value of \(p\) ． The line \(L _ { 3 }\) has equation \(\mathbf { r } = \left( \begin{array} { r } - 15
12
- 9 \end{array} \right) + u \left( \begin{array} { r } 8
- 6
- 5 \end{array} \right)\) and the lines \(L _ { 3 }\) and \(L _ { 2 }\) intersect at the point \(A\) ．
The point \(B\) on \(L _ { 2 }\) has position vector \(\left( \begin{array} { r } 5
- 13
1 \end{array} \right)\) and point \(C\) lies on \(L _ { 3 }\) such that \(A B D C\) is a rhombus．
（b）Find the two possible position vectors of \(D\) ．