Position vector question

[dekoyl]

The position vectors of points A and B, relative to origin O, are a and b representively where a and b are non-zero, non parallel vectors. The point P is such that . The mindpoint of AB is the point Q. The point R is such at .

1. Find in terms of a and b:
2. Show that R lies on AP and state the ratio AR:RP

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I just have difficulty picturing this question. It's okay if question 2 isn't attempted but I just need a start =( (Question 1 is only one part of (a) too)

Thanks

[Mao]

1)
RP = RO + OP = -1.6 OQ + 4OB = -1.6*0.5*(OA + OB) + 4 OB = 4.8 OB - 0.8 OA = 3.2b - 0.8a

2)
AP = AO + OP = 4b - a
here, we notice that RP is 0.8AP (and they point to the same direction), hence R must lie on AP

AR:RP
0.2:0.8
1  : 4

[dekoyl]

Ah thank you Mao

Initially I didn't pick up that 0.5(OA + OB) = OQ :[

Thanks again