If G is the centroid of a triangle ABC, then $\vec {GA} +\vec{GB}+\vec{GC}$ equals
Answer & explanation
Correct answer: option 1
We have,
$\vec {GB}+\vec {GC}=(1+1)\vec {GD}$
$⇒\vec {GB}+\vec {GC}=2\vec {GD}$, where D is the mid-point of BC.
$⇒\vec {GA}+\vec {GB}+\vec {GC}=\vec {GA}+2\vec {GD}$
∵ G divides AD in the ratio 2 : 1 $∴ 2 \vec {GD} =-\vec {GA}$
$∴\vec {GA} +\vec{GB}+\vec{GC}=\vec {GA}-\vec {GA}$