3．The lines \(L _ { 1 }\) and \(L _ { 2 }\) have equations given by
\(L _ { 1 } : \quad \mathbf { r } = \left( \begin{array} { c } - 7
7
1 \end{array} \right) + \lambda \left( \begin{array} { c } 2
0
- 3 \end{array} \right)\) and \(L _ { 2 } : \quad \mathbf { r } = \left( \begin{array} { c } 7
p
- 6 \end{array} \right) + \mu \left( \begin{array} { c } 10
- 4
- 1 \end{array} \right)\)
where \(\lambda\) and \(\mu\) are parameters and \(p\) is a constant．
The two lines intersect at the point \(C\) ．
（a）Find
（i）the value of \(p\) ，
（ii）the position vector of \(C\) ．
（b）Show that the point \(B\) with position vector \(\left( \begin{array} { c } - 13
11
- 4 \end{array} \right)\) lies on \(L _ { 2 }\) ． The point \(A\) with position vector \(\left( \begin{array} { c } - 7
7
1 \end{array} \right)\) lies on \(L _ { 1 }\) ．
（c）Find \(\cos ( \angle A C B )\) ，giving your answer as an exact fraction． The line \(L _ { 3 }\) bisects the angle \(A C B\) ．
（d）Find a vector equation of \(L _ { 3 }\) ．