7. The point \(A\) with coordinates ( \(- 3,7,2\) ) lies on a line \(l _ { 1 }\) The point \(B\) also lies on the line \(l _ { 1 }\)
Given that \(\quad \overrightarrow { A B } = \left( \begin{array} { r } 4
- 6
2 \end{array} \right)\),
- find the coordinates of point \(B\).
The point \(P\) has coordinates ( \(9,1,8\) )
- Find the cosine of the angle \(P A B\), giving your answer as a simplified surd.
- Find the exact area of triangle \(P A B\), giving your answer in its simplest form.
The line \(l _ { 2 }\) passes through the point \(P\) and is parallel to the line \(l _ { 1 }\)
- Find a vector equation for the line \(l _ { 2 }\)
The point \(Q\) lies on the line \(l _ { 2 }\)
Given that the line segment \(A P\) is perpendicular to the line segment \(B Q\),
- find the coordinates of the point \(Q\).