10 The straight line \(l\) passes through the points \(A\) and \(B\) with position vectors
$$2 \mathbf { i } + 2 \mathbf { j } + \mathbf { k } \quad \text { and } \quad \mathbf { i } + 4 \mathbf { j } + 2 \mathbf { k }$$
respectively. This line intersects the plane \(p\) with equation \(x - 2 y + 2 z = 6\) at the point \(C\).
- Find the position vector of \(C\).
- Find the acute angle between \(l\) and \(p\).
- Show that the perpendicular distance from \(A\) to \(p\) is equal to 2 .