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Prove that GvecA+GvecB+GvecC=vec0, if G ...

Prove that `GvecA+GvecB+GvecC=vec0`, if G is the centroid of `Delta` ABC.

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Let `veca,vecb` and `vecc` be the position vectors of the vertices A,B and C of a triangle ABC, respectively. Then the position vector of the centroid G is `(veca+vecb+vecc)/(3)`
Now `GvecA+GvecB+GvecC`
`=veca-((veca+vecb+vecc)/(3))+vecb((veca+vecb+vecc)/(3))+vecc((veca+vecb+vecc)/(3))`
`=(veca+vecb+vecc)-(veca+vecb+vecc)=vec0`
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