The points A, B, C have position vectors

\(2\mathbf{i} + 2\mathbf{j}, \quad -\mathbf{j} + \mathbf{k} \quad \text{and} \quad 2\mathbf{i} + \mathbf{j} - 7\mathbf{k}\)

respectively, relative to the origin O.

(a) Find an equation of the plane OAB, giving your answer in the form \(\mathbf{r} \cdot \mathbf{n} = p\).

The plane \(\Pi\) has equation \(x - 3y - 2z = 1\).

(b) Find the perpendicular distance of \(\Pi\) from the origin.

(c) Find the acute angle between the planes OAB and \(\Pi\).

(d) Find an equation for the common perpendicular to the lines OC and AB.