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Vector Proof Question!

  1. Mar 25, 2007 #1
    Hey ive got a vector proof question that i cant get. Sorry i cant provide a diagram but hopefully you can see where i went wrong.
    1. The problem statement, all variables and given/known data
    For triange PQR with with X dividing vector PR in the ratio of 2:3, Y the midpoint of vector PQ and Z the pint of intersection of QX and RY prove that Z divides RY in the ratio 3:1

    2. Relevant equations
    first i said that vector RZ was a scalar multiple of vector RY.

    and my second equation was RZ=tRQ + (1-t)RX

    3. The attempt at a solution

    first i got both equations in terms of sides of the triange.
    and RZ=tRQ +(1-t)3/5(RP)

    then i set the two equations equal to each other and attempted to solve for s and t. I ended up getting s=6/5 and t=2/3. Any help?
  2. jcsd
  3. Mar 27, 2007 #2


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    You can make your job a lot easier by placing one of the vertices at the origin. So say P=0. Now you can take R and Q to be linearly independent and just equate coefficients of R and Q.
  4. Mar 27, 2007 #3
    ok thanks, does it matter which point i use? not only for this question but others like it?
  5. Mar 27, 2007 #4


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    No, clearly it can't matter. Try it two different ways if you are having doubts.
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