Question

If D, E and F be the middle points of the sides BC,CA and AB of the `DeltaABC`, then `AD+BE+CF` is

Answer 1

Correct Answer - A
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`