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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`

A

`vec0`

B

`3 vec(GA)`

C

`3 vec(GB)`

D

`3 vec(GC)`

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Verified by Experts

The correct Answer is:
A
We have `vec(GB) + vec(GC) = (1+1) vec(GD) = 2vec(GD)`, where D is the midpoint of BC. Therefore,
`vec(GA) = vec(GB) +vec(GC) = vec(GA)+ 2vec(GD) `
`" "= vec(GA) - vec(GA) =0`
`(because G` divides AC in the ratio `2:1, therefore 2 vec(GD)=- vec(GA))`
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