9 With respect to the origin \(O\), the point \(A\) has position vector given by \(\overrightarrow { O A } = \mathbf { i } + 5 \mathbf { j } + 6 \mathbf { k }\). The line \(l\) has vector equation \(\mathbf { r } = 4 \mathbf { i } + \mathbf { k } + \lambda ( - \mathbf { i } + 2 \mathbf { j } + 3 \mathbf { k } )\).
- Find in degrees the acute angle between the directions of \(O A\) and \(l\).
- Find the position vector of the foot of the perpendicular from \(A\) to \(l\).
- Hence find the position vector of the reflection of \(A\) in \(l\).