Let `D ,Ea n dF` be the middle points of the sides `B C ,C Aa n dA B ,` respectively of a triangle `A B Cdot` Then prove that ` vec A D+ vec B E+ vec C F= vec0` .

Options

A. `vec(0)`
B. 0
C. 2
D. none of these

Answer

A

Explanation

Let the position vectors of A, B, C be ` vec(a), vec(b) and vec(c ) ` respectively. Then position vectors of D, E and F are
`(vec(b)+vec(c))/(2),(vec(c)+vec(a))/(2) and (vec(a)+vec(b))/(2)`
`vec(AD)+vec(BE)+vec(CF)`
`={(vec(b)+vec(c))/(2)-vec(a)}+{(vec(c)+vec(a))/(2)-vec(b)} +{(vec(a)+vec(b))/(2)-vec(c)}=vec(0)`