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If A, B, C are the vertices of a triangl...

If `A, B, C` are the vertices of a triangle whose position vectros are `vec a,vec b, vec c and G` is the centroid of the `DeltaABC,` then `overline(GA)+overline(GB)+overline(GC) =`

A

0

B

`A+B+C`

C

`(a+b+c)/(3)`

D

`(a+b-c)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
Position vectors of vertices A,B and C of the `DeltaABC=a,b and c`. We know that, position vector of centroid of the triangle,
`G=(a+b+c)/(3)`.
Therefore, GA+GB+GC
`=(a-(a+b+c)/(3))+(b-(a+b+c)/(3))+(c-(a+b+c)/(3))`
`=(1)/(3)(2a-b-c+2b-a-c+2c-a-b)=0`.
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