In the diagram, OABCDEFG is a cuboid in which OA = 3 units, OC = 2 units and OD = 2 units. Unit vectors i, j and k are parallel to OA, OD and OC respectively. M is the midpoint of EF.

(a) Find the position vector of M.

The position vector of P is i + j + 2k.

(b) Calculate angle PAM.

(c) Find the exact length of the perpendicular from P to the line passing through O and M.