Question

If $G$ is the centroid of $\Delta ABC$ and $O$ is any point then $\overline{OA}+\overline{OB}+\overline{OC}=$

• A. $\overline{OG}$
• B. $2\overline{OG}$
• C. $3\overline{OG}$
• D. $4\overline{OG}$

Answer 1

The correct option is C $3\overline{OG}$

Let $O$ be the origin

Then from the triangle we get

$\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}=\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}$

$\overrightarrow{OG}=\frac{\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}}{3}$

$\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}=3\overrightarrow{OG}$

Hence, the option $D$ is the correct answer.