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If G is the centroid of a triangle A B C...

If `G` is the centroid of a triangle `A B C ,` prove that ` vec G A+ vec G B+ vec G C= vec0dot`

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Let edges of the triangle be `veca,vecb` and `vecc`
`vec{GA}=(veca-frac{veca+vecb+vecc}{3})=frac{2veca-vecb-vecc}{3}`
`vec{GB}=frac{2vecb-veca-vecc}{3}`
`vec{GC}=frac{2vecc-veca-vecb}{3}`
`implies vec{GA}+vec{GB}+vec{GC}=vec0`
Hence Proved.
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