If A,B and C are the points P and Q are p and q respectively is another point with position vector r = 3q – ½ p.
Express in terms of p and q.
i) PR
ii) RQ hence shows that P, Q and R are collinear.
iii) Determine the ratio PQ: QR.
I can't figure out what A,B,C have to do with P,Q,R.
PR = r-p = 3q-p/2 - p = 3q - 3/2 p
RQ = q-r = q-(3q - 1/2 p) = -2q + 1/2 p
I don't see that they are collinear.
If we let
p = 2j
q = i
then p and q are not collinear, and r=3i-j is not collinear with either p or q.
The three vectors are coplanar, since r is a linear combination of p and q.
I suspect there is something missing from the problem here.
I expect you can find PQ:QR