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.
Since OACB forms a parallelogram,
and are parallel with a common point N.
Thus, A, B, and N are collinear.