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.
and 
are parallel with a common point N.
![[\frac{1}{2}\vec{OA} + \lambda (\vec{AB}) - \frac{1}{2}\vec{OC}] \bullet \vec{AB} = 0](https://theculture.sg/wp-content/ql-cache/quicklatex.com-db8551f272cfc72b79633ecf4735cc6d_l3.png "Rendered by QuickLaTeX.com")
