9 The points \(A\) and \(B\) lie on the line \(l _ { 1 }\) and have coordinates \(( 2,5,1 )\) and \(( 4,1 , - 2 )\) respectively.
- Find the vector \(\overrightarrow { A B }\).
- Find a vector equation of the line \(l _ { 1 }\), with parameter \(\lambda\).
- The line \(l _ { 2 }\) has equation \(\mathbf { r } = \left[ \begin{array} { r } 1
- 3
- 1 \end{array} \right] + \mu \left[ \begin{array} { r } 1
0
- 2 \end{array} \right]\).
- Show that the point \(P ( - 2 , - 3,5 )\) lies on \(l _ { 2 }\).
- The point \(Q\) lies on \(l _ { 1 }\) and is such that \(P Q\) is perpendicular to \(l _ { 2 }\). Find the coordinates of \(Q\).