If D , E and F are respectively mid-points of A B , A C and B C in ∆ A B C , then B E → + A F → is equal to

Step-by-step solution

Given, D ,   E and F are respectively mid-points of A B ,   A C and B C of ∆ A B C . Let O A → = a → ,   O B → = b → and   OC → = c → ,   then by using the mid-point formula, we have O D → = a → + b → 2 ,   O E → = a → + c → 2 and O F → = b → + c → 2 . Now A F → = O F → - O A → = 1 2 b → + c → - a → ,   B E → = O E → - O B → = 1 2 a