Q74 / 125 · BITSAT 2018 · Mathematics

In a $∆ A B C,$ $D, E, F$ are the mid-points of the sides $B C$ , $C A$ and $A B$ respectively, the vector $\vec{A D}$ is equal to

Solution

$\vec{A D} = 3 \vec{G D}$

$= 3 \cdot \frac{1}{2} (\vec{G B} + \vec{G C})$

$= \frac{3}{2} (\frac{2}{3} \vec{E B} + \frac{2}{3} \vec{F C})$

$= - \vec{B E} - \vec{C F}$

Hence, option (d) is correct.

Hence, the correct answer is option: 'D'.