8. Relative to a fixed origin \(O\), the point \(A\) has position vector \(\left( \begin{array} { r } - 2
4
7 \end{array} \right)\) and the point \(B\) has position vector \(\left( \begin{array} { r } - 1
3
8 \end{array} \right)\) The line \(l _ { 1 }\) passes through the points \(A\) and \(B\).

1. Find the vector \(\overrightarrow { A B }\).
2. Hence find a vector equation for the line \(l _ { 1 }\) The point \(P\) has position vector \(\left( \begin{array} { l } 0
   2
   3 \end{array} \right)\)
   Given that angle \(P B A\) is \(\theta\),
3. show that \(\cos \theta = \frac { 1 } { 3 }\) The line \(l _ { 2 }\) passes through the point \(P\) and is parallel to the line \(l _ { 1 }\)
4. Find a vector equation for the line \(l _ { 2 }\) The points \(C\) and \(D\) both lie on the line \(l _ { 2 }\)
   Given that \(A B = P C = D P\) and the \(x\) coordinate of \(C\) is positive,
5. find the coordinates of \(C\) and the coordinates of \(D\).
6. find the exact area of the trapezium \(A B C D\), giving your answer as a simplified surd.