Proving a 2:1 ratio triangle having a Zero Vector

[aeromat]

Homework Statement

I need help once again with this question below:

Thanks,
aeromat

The Attempt at a Solution

This is what I have so far:
GP = GQ + QP
GQ = GP + PQ
GR = GP + PR

GP + GQ + GR = GQ + QP[-] + PQ[+] + GP + PR + GP
GP + GQ + GR = GQ + 2GP + PR

I am stuck now. I took the approach of taking GP + GQ + GR individually and finding their vector components.

 

[praharmitra]

you haven't used the 2:1 ratio fact anywhere. try using that.

hint: name the mid points of each side A,B,C. And try to use GA, GB, GC in your equations.