The points A, B, C have position vectors

\(4\mathbf{i} - 4\mathbf{j} + \mathbf{k}\),\( \quad -4\mathbf{i} + 3\mathbf{j} - 4\mathbf{k}\), \(\quad 4\mathbf{i} - \mathbf{j} - 2\mathbf{k}\),

respectively, relative to the origin O.

(a) Find the equation of the plane ABC, giving your answer in the form \(ax + by + cz = d\).

(b) Find the perpendicular distance from O to the plane ABC.

(c) The point D has position vector \(2\mathbf{i} + 3\mathbf{j} - 3\mathbf{k}\).

Find the coordinates of the point of intersection of the line OD with the plane ABC.