1. The line \(l _ { 1 }\) has equation \(\mathbf { r } = \left( \begin{array} { r } 2
   3
   - 7 \end{array} \right) + \lambda \left( \begin{array} { l } 1
   2
   2 \end{array} \right)\) where \(\lambda\) is a scalar parameter.

The line \(l _ { 2 }\) has equation \(\mathbf { r } = \left( \begin{array} { r } 2
3
- 7 \end{array} \right) + \mu \left( \begin{array} { r } 4
- 1
8 \end{array} \right)\) where \(\mu\) is a scalar parameter.
Given that \(l _ { 1 }\) and \(l _ { 2 }\) meet at the point \(P\)

1. state the coordinates of \(P\) Given that the angle between lines \(l _ { 1 }\) and \(l _ { 2 }\) is \(\theta\)
2. find the value of \(\cos \theta\), giving the answer as a fully simplified fraction. The point \(Q\) lies on \(l _ { 1 }\) where \(\lambda = 6\)
   Given that point \(R\) lies on \(l _ { 2 }\) such that triangle \(Q P R\) is an isosceles triangle with \(P Q = P R\)
3. find the exact area of triangle \(Q P R\)
4. find the coordinates of the possible positions of point \(R\)