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

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Homework Help Overview

The discussion revolves around a vector proof problem involving triangle PQR, where the task is to prove that point Z divides segment RY in a 3:1 ratio. The original poster describes their attempts to establish relationships between the vectors involved, particularly focusing on the points X, Y, and Z.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to express vector relationships using scalar multiples and equations derived from the triangle's sides. Some participants suggest simplifying the problem by placing one vertex at the origin and question the impact of choosing different points for analysis.

Discussion Status

The discussion is ongoing, with participants exploring different methods to approach the problem. Some guidance has been offered regarding the placement of points to simplify calculations, and there is an acknowledgment of the validity of trying multiple approaches.

Contextual Notes

There is a mention of the original poster's inability to provide a diagram, which may affect the clarity of the discussion. The problem also involves specific ratios and relationships that are central to the proof being sought.

ehjay01
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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?
 
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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.
 
ok thanks, does it matter which point i use? not only for this question but others like it?
 
ehjay01 said:
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.
 

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