99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

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

Options

AD C
B1 2 B F
C2 B F
D3 2 B F

Correct answer

A. D C

Step-by-step solution

Let A= a , B= b , C= c Now, A F = 1 2 ( b + c )- a B E = 1 2 ( a + c )- b and C D = 1 2 ( a + b )- c A F + B E = 1 2 ( b + c )- a + 1 2 ( a + c )- b =- 1 2 b - 1 2 a + c = c - 1 2 ( a + b )= D C

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