7. Two lines, \(l _ { 1 }\) and \(l _ { 2 }\), have the following equations.
$$\begin{aligned}
& l _ { 1 } : \mathbf { r } = \left( \begin{array} { c }
- 11
10
3
\end{array} \right) + \lambda \left( \begin{array} { c }
2
- 2
1
\end{array} \right)
& l _ { 2 } : \mathbf { r } = \left( \begin{array} { l }
5
2
4
\end{array} \right) + \mu \left( \begin{array} { c }
3
1
- 2
\end{array} \right)
\end{aligned}$$
\(P\) is the point of intersection of \(l _ { 1 }\) and \(l _ { 2 }\).
- Find the position vector of \(P\).
- Find, correct to 1 decimal place, the acute angle between \(l _ { 1 }\) and \(l _ { 2 }\). \(Q\) is a point on \(l _ { 1 }\) which is 12 metres away from \(P . R\) is the point on \(l _ { 2 }\) such that \(Q R\) is perpendicular to \(l _ { 1 }\).
- Determine the length \(Q R\).
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