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

Question

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, D C →, 3 2 B F →, 1 2 B F →, 1 2 D C →

MARKS App · Accepted Answer

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 → + c → - b → and C D → = O D → - O C → = 1 2 a → + b → - c → . ∴ A F → + B E → = 1 2 b → + c → - a → + 1 2 a → + c → - b → = - 1 2 a → + b → + c → = - C D → = D C → .

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