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: PA2+PB2+PO2=GA2+GB2+GO2+3 (PG2) 3. 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?