
vectors help,
The points O; A and B do not lie in a straight line.
OA = a and OB = b.
P is the midpoint 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 $\displaystyle \lambda $ and $\displaystyle \mu $ such that
$\displaystyle RQ = \lambda AQ $
and $\displaystyle PR = \mu PB $
Hence find an expression for PQ in terms of a; b; $\displaystyle \lambda , \mu $ and
By equating the coecients of a and of b in two expressions for vector PQ, find $\displaystyle \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?