9 Relative to the origin \(O\), the point \(A\) has position vector given by \(\overrightarrow { O A } = \mathbf { i } + 2 \mathbf { j } + 4 \mathbf { k }\). The line \(l\) has equation \(\mathbf { r } = 9 \mathbf { i } - \mathbf { j } + 8 \mathbf { k } + \mu ( 3 \mathbf { i } - \mathbf { j } + 2 \mathbf { k } )\).

1. 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 \(l\).
2. Find the equation of the plane through the origin which contains \(l\). Give your answer in the form \(a x + b y + c z = d\).
3. Find the exact value of the perpendicular distance of \(A\) from this plane.