(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img147.imageshack.us/img147/733/vectorsba4.png [Broken]

Given is the triangle OAB and a variable point P. G is the centroid. Prove that:

PA^{2}+PB^{2}+PO^{2}=GA^{2}+GB^{2}+GO^{2}+3 (PG^{2})

3. The attempt at a solution

I treat O as the origin.

Vectors are denoted in bold.

Position vectors of A, B, P area,bandprespectively.

G=a+b/3

How on earth am I going to prove that:

9(|p-a|^{2}+|p-b|^{2}+|p|^{2})=|b-2a|^{2}+|a-2b|^{2}+|a+b|^{2}+3|a+b-3p|^{2}

I mean is there any criteria to prove this equation in modulus of vectors when I dont know the angles between any of them?

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# Homework Help: Vectors - Prove the following relation about the centroid

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