In a ∆ ABC, D, E, F are the mid-points of the sides BC , CA and AB...

In a

∆ ABC, D, E, F

are the mid-points of the sides

BC

CA

and

AB

respectively, the vector

\overset{→}{AD}

is equal to In a ∆ ABC, D, E, F are the mid-points of the sides BC , CA and AB respectively, the vector → AD is equal to

Options

A $\overset{→}{BE} + \overset{→}{CF}$
B $\overset{→}{BE} - \overset{→}{CF}$
C $\overset{→}{CF} - \overset{→}{BE}$
D $- \overset{→}{BE} - \overset{→}{CF}$

Correct answer

D. $- \overset{→}{BE} - \overset{→}{CF}$

Step-by-step solution

In a ∆ ABC, D, E, F are the mid-points of the sides BC , CA and AB respectively, the vector → AD is equal to

$\overset{→}{AD} = 3\overset{→}{GD}$

$= 3 \cdot \dfrac{1}{2} \left(\overset{→}{GB} + \overset{→}{GC}\right)=\dfrac{3}{2} \left(\dfrac{2}{3}\overset{→}{EB} + \dfrac{2}{3}\overset{→}{FC}\right)$ = - \overset{→}{BE} - \overset{→}{CF} $Hence, option (d) is correct.$

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