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 $60^{\circ}, |a|=2 \text{~and~} |b|=3$, find the position vector of P in terms of a and b.