Question

$ABC$ is a $\Delta$ and $G$ is its centroid. If $\overline{AB}=\overline{b}$ and $\overline{AC}=\overline{c}$, then $\overline{AG}$ is equal to

• A. $\frac{2}{3}(\overline{b}+\overline{c})$
• B. $\overline{b}+\overline{c}$
• C. $\frac{1}{3}(\overline{b}+\overline{c})$
• D. $\frac{3}{2}(\overline{b}+\overline{c})$

Answer 1

The correct option is C $\frac{1}{3}(\overline{b}+\overline{c})$

Taking $A$ as origin.
So, position vector of $B=\overline{AB}=\overline{b}$
and position vector of $C=\overline{AC}=\overline{c}$
Hence by centroid formula,

$\overline{AG}$ = position vector of $G$ $=\frac{\overline{a}+\overline{b}+\overline{c}}{3}$

$=\frac{\overline{b}+\overline{c}}{3}$