NYJC P1 Q4

Referred to the origin , the points A and B have position vectors **a** and **b** respectively. A point C is such that OACB forms a parallelogram. Given that M is the mid-point of AC, find the position vector of point N if M lies on ON produced such that OM:ON is in ratio 3:2. Hence show that A, B, and N are collinear.

Point P is on AB such that MP is perpendicular to AB. Given that angle AOB is , find the position vector of P in terms of **a** and **b**.