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JEE Main202315 Apr 2023Morning ShiftMathematicsVector AlgebraActual

Let A B C D be a quadrilateral. If E and F are the mid points of the diagonals A C and B D respectively and A B → - B C → + A D → - D C → = k F E → , then k is equal to

Options

  1. A4
  2. B- 2
  3. C2
  4. D- 4

Correct answer

D. - 4

Step-by-step solution

Given, A B C D be a quadrilateral. If E and F are the mid points of the diagonals A C and B D respectively and A B → -   B C → + A D → - D C → = k   F E → , Now plotting the diagram we get, Now let position vector of A ,   B ,   C and D are a , →   b , →   c → and d → respectively Now by midpoint formula, Position vector of E = O C → + O A → 2 = c → + a → 2 And Position vector of F = b → + d → 2 N

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