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ritwik06
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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:
PA2+PB2+PO2=GA2+GB2+GO2+3 (PG2)
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 don't know the angles between any of them?
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