# Math Help - vectors help,

1. ## vectors help,

The points O; A and B do not lie in a straight line.

OA = a and OB = b.
P is the mid-point of OA. Q lies on the line segment OB, such that
OQ : OB = 1 : 3. AQ and BP intersect at R.
(a) Express the vectors
AB; AQ; PB and PQ in terms of a and b.

explain why there are scalars $\lambda$ and $\mu$ such that
$RQ = \lambda AQ$
and $PR = \mu PB$

Hence find an expression for PQ in terms of a; b; $\lambda , \mu$ and
By equating the coecients of a and of b in two expressions for vector PQ, find $\lambda , \mu$ and Hence show that AR : RQ = 3 : 2 and find the ratio P R : RB.

Can someone check to see if these are correct?

AB = -a + b

AQ = -a + 1/3b

PB = 1/2a + b

PQ = 1/2a + 1/3b

I am bit stuck on the second part, I know their are scalars, because the both vectors are the same, but have different magnitudes?