With respect to the origin O, the points A, B and C have position vectors given by \(\overrightarrow{OA} = \mathbf{i} - \mathbf{k}\), \(\overrightarrow{OB} = 3\mathbf{i} + 2\mathbf{j} - 3\mathbf{k}\) and \(\overrightarrow{OC} = 4\mathbf{i} - 3\mathbf{j} + 2\mathbf{k}\).

The mid-point of AB is M. The point N lies on AC between A and C and is such that \(AN = 2NC\).

(i) Find a vector equation of the line MN.

(ii) It is given that MN intersects BC at the point P. Find the position vector of P.