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Triangle Vector Problem

  1. Jan 18, 2007 #1
    1. The problem statement, all variables and given/known data
    Consider the triangle ABC whose vertices have position vectors a, b, and c respectively.


    Find the position vector of
    (a) P, the mid-point of AB
    (b) Q, the point of trisection of AB, with Q closer to B.
    (c) R, the mid-point of the median CP.

    2. Relevant equations
    None really. It just seems that I have a major conflict with the textbook answer and I'm not quite sure why. The textbook says:
    (a) ½(b + a)
    (b) ⅓(2b + a)
    (c) ½(a + b + c)

    3. The attempt at a solution
    (a) I got this answer. Looking at the diagram, if we theoretically add OB and OA tip-to-tail, the half of the resultant vector should give us OP.
    (b) Similarly to (a),
    AB = b + a
    OQ = ⅓AB
    --> OQ = ⅓(b + a)
    I don't see why b is multiplied by 2.

    (c) First off:
    CP = CO + OP
    CP = -c + ½(b + a)

    OR = OC + ½CP
    OR = c + ½(-c + ½(b + a))
    OR = ½c + ¼b + ¼a

    Yeah, I don't see why my answers disagree with the textbook.
  2. jcsd
  3. Jan 18, 2007 #2


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    Homework Helper

    a) OB = OA + AB
    b = a + AB
    AB = b - a, not b + a

    OP = OA + ½(AB) = a + ½(b - a) = a + ½b - ½a
    OP = ½(b + a)

    b) OQ = OA + (2/3)AB (Q is 2/3 of way along AB)

    c) the book is wrong, you are right!!
    Last edited: Jan 18, 2007
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