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AP EAMCET201921 Apr 2019Evening ShiftMathematicsVector AlgebraActual

Let D and E be the midpoints of the sides A C and B C of a triangle A B C respectively. If O is an interior point of the triangle A B C such that O A → + 2 O B → + 3 O C → = 0 → , then the area (in sq. units) of the triangle O D E is

Options

  1. A6
  2. B5
  3. C3 4
  4. D0

Correct answer

D. 0

Step-by-step solution

It is given that, O A → + 2 O B → + 3 O C → = 0 The figure below represents the triangle A B C and midpoints. Ar △ O D E = 1 2 | O D → × O E → | = 1 2 a → + c → 2 × b → + c → 2 = 1 8 ( a → × b → + a → × c → + c → × b → )     . . . i The given equation can be written as, a → + 2 b → + 3 c → = 0 →     . . . ii Multiply b → in equation ii we get, a &

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