With respect to the origin O, the points A and B have position vectors given by \(\overrightarrow{OA} = \mathbf{i} + 2\mathbf{j} + 2\mathbf{k}\) and \(\overrightarrow{OB} = 3\mathbf{i} + 4\mathbf{j}\). The point P lies on the line AB and OP is perpendicular to AB.

(i) Find a vector equation for the line AB.

(ii) Find the position vector of P.