Let G be the centroid of ΔABC. If $\vec{AB} = \vec a, \vec{AC} = \vec b$, then $\vec{AG}$, in terms of $\vec a$ and $\vec b$, is
Answer & explanation
Correct answer: option 3
Let A be the origin. Then, $\vec{AB} = \vec a, \vec{AC} = \vec b$ implies that the position vectors of B and C are $\vec b$ and $\vec c$ respectively. Let AD be the median and G be the centroid. Then,
P.V. of $D+\frac{\vec a+\vec b}{2}$, P.V. of $G=\frac{\vec a+\vec b}{3}$
$∴\vec{AG}=\frac{\vec a+\vec b}{3}$