10 The lines \(l\) and \(m\) have vector equations
$$\mathbf { r } = \mathbf { i } - 2 \mathbf { k } + s ( 2 \mathbf { i } + \mathbf { j } + 3 \mathbf { k } ) \quad \text { and } \quad \mathbf { r } = 6 \mathbf { i } - 5 \mathbf { j } + 4 \mathbf { k } + t ( \mathbf { i } - 2 \mathbf { j } + \mathbf { k } )$$
respectively.
- Show that \(l\) and \(m\) intersect, and find the position vector of their point of intersection.
- Find the equation of the plane containing \(l\) and \(m\), giving your answer in the form \(a x + b y + c z = d\).