Let D, E and F be the middle points of the sides BC,CA and AB respectively of a triangle ABC. Then, AD + BE + CF equals to

Options

A. 0
B. 0
C. 2
D. None of these

Answer

A

Explanation

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