8. With respect to a fixed origin \(O\), the lines \(l _ { 1 }\) and \(l _ { 2 }\) are given by the equations
$$l _ { 1 } : \mathbf { r } = \left( \begin{array} { r }
1
- 3
2
\end{array} \right) + \lambda \left( \begin{array} { l }
1
2
3
\end{array} \right) , \quad l _ { 2 } : \mathbf { r } = \left( \begin{array} { l }
6
4
1
\end{array} \right) + \mu \left( \begin{array} { r }
1
1
- 1
\end{array} \right)$$
where \(\lambda\) and \(\mu\) are scalar parameters.
- Show that \(l _ { 1 }\) and \(l _ { 2 }\) do not meet.
The point \(P\) is on \(l _ { 1 }\) where \(\lambda = 0\), and the point \(Q\) is on \(l _ { 2 }\) where \(\mu = - 1\)
- Find the acute angle between the line segment \(P Q\) and \(l _ { 1 }\), giving your answer in degrees to 2 decimal places.
- Find the shortest distance from the point \(Q\) to the line \(l _ { 1 }\), giving your answer to 3 significant figures.