If A,B and C are the vertices of a triangle with position vectors `vec(a) , vec(b) ` and `vec(c )` respectively and G is the centroid of `Delta ABC`, then `vec( GA) + vec( GB ) + vec( GC )` is equal to

Options

A. 0
B. `A+B+C`
C. `(a+b+c)/(3)`
D. `(a+b-c)/(3)`

Answer

A

Explanation

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`.