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## Homework Statement

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})

## The Attempt at a Solution

I treat O as the origin.

Vectors are denoted in bold.

Position vectors of A, B, P are

**a,b**and

**p**respectively.

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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