How to Solve a Vector Proof Question: Proving Z Divides RY in a 3:1 Ratio

[ehjay01]

Hey I've got a vector proof question that i can't get. Sorry i can't provide a diagram but hopefully you can see where i went wrong.

Homework Statement

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

Homework Equations

first i said that vector RZ was a scalar multiple of vector RY.
RZ=sRY

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

The Attempt at a Solution

first i got both equations in terms of sides of the triange.
RZ=s(RQ+1/2QP),
and RZ=tRQ +(1-t)3/5(RP)
RZ=tRQ+3/5(1-t)(RQ+QP)

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?

 

[Dick]

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.

 

[ehjay01]

ok thanks, does it matter which point i use? not only for this question but others like it?

 

[Dick]

ok thanks, does it matter which point i use? not only for this question but others like it?

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