9 The equations of two straight lines \(l _ { 1 }\) and \(l _ { 2 }\) are $$l _ { 1 } : \quad \mathbf { r } = \mathbf { i } - 2 \mathbf { j } + 3 \mathbf { k } + \lambda ( 2 \mathbf { i } - \mathbf { j } + a \mathbf { k } ) \quad \text { and } \quad l _ { 2 } : \quad \mathbf { r } = - \mathbf { i } - \mathbf { j } - \mathbf { k } + \mu ( 3 \mathbf { i } - 2 \mathbf { j } - 2 \mathbf { k } ) ,$$ where \(a\) is a constant.
The lines \(l _ { 1 }\) and \(l _ { 2 }\) are perpendicular.

1. Show that \(a = 4\).
   The lines \(l _ { 1 }\) and \(l _ { 2 }\) also intersect.
2. Find the position vector of the point of intersection.
   The point \(A\) has position vector \(- 5 \mathbf { i } + \mathbf { j } - 9 \mathbf { k }\).
3. Show that \(A\) lies on \(l _ { 1 }\).
   The point \(B\) is the image of \(A\) after a reflection in the line \(l _ { 2 }\).
4. Find the position vector of \(B\).