With respect to the origin O, the points A and B have position vectors given by \(\overrightarrow{OA} = 6\mathbf{i} + 2\mathbf{j}\) and \(\overrightarrow{OB} = 2\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}\). The midpoint of OA is M. The point N lying on AB, between A and B, is such that \(AN = 2NB\).

(a) Find a vector equation for the line through M and N.

The line through M and N intersects the line through O and B at the point P.

(b) Find the position vector of P.

(c) Calculate angle OPM, giving your answer in degrees.