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Aabha Mall
Asked: 2022-11-08T12:56:21+05:30 In:

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) =`

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) =`
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  1. Correct Answer – 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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