N2005 P1 Q14

The lines \(l_1\) and \(l_2\) have equations

\[\mathbf{r} = \begin{pmatrix} 0 \\ 1 \\ 2 \end{pmatrix} + s \begin{pmatrix} 1 \\ 0 \\ 3 \end{pmatrix} \text{ and}\hspace{0.5em} \mathbf{r} = \begin{pmatrix} -2 \\ 3 \\ 1 \end{pmatrix} + t \begin{pmatrix} 2 \\ b \\ 0 \end{pmatrix}\]

respectively, where \(b\) is a constant.

1. For the case where the lines intersect, calculate the acute angle between them.
2. For the case when \(b = 1\), find the position vectors of the points \(P\) on \(l_1\) and \(Q\) on \(l_2\) such that \(O\), \(P\) and \(Q\) are collinear, where \(O\) is the origin.