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Math Help - vectors help,

  1. #1
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    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?
    Last edited by Tweety; November 14th 2012 at 06:35 AM.
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