G is a point inside the plane of the triangle `ABC, vecGA + vecGB + vecGC=0`, then show that G is the centroid of triangle ABC.

Options

A. `vec(0)`
B. `3vec(GA)`
C. `3 G vec(B)`
D. `3 vec(GC)`

Answer

A

Explanation

We have,
`G vec(B)+G vec(C ) =(1+1)vec(GD)`
`rArr G vec(B) + G vec(C ) =2 vec(GD)`, where D is the mid point of BC.
`rArr G vec(A) + G vec(B) + G vec(C ) =Gvec(A) +2 vec(GD) `
` because ` G divides AD in the ratio `2 : 1 therefore 2 vec(GD) = -G vec(A)`
`therefore G vec(A) +G vec(B) + G vec(C ) =G vec(A) - G vec(A) = vec(0)`