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

My answers:

a) x=3/2b-1/2a

b) y=1/3c+3/4b

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