I was wondering if you guys could help me with this question.
The question is:
The points A, B and C have position vector of a, b and c respectively referred to an origin O.
a) Given the point X lies on AB produced so that AB:BX=2:1, find x, the position vector of X, in terms of a and b
b) If Y lies on BC, between B and C so that BY:YC=1:3, find y, the positoin vector of Y, in terms of b and c.
c) Given that Z is the mid-point of AC, show that X, Y, and Z are collinear
d) Calculate XY:YZ
c) I don't know how to do this one, since I don't know how to get them to be scalar multiples. By the way, this is what I think the question is like. I'm guessing I don't understand the question cause I don't see how the points could be collinear.
Thanks in advance