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JEE Main202429 Jan 2024Evening ShiftMathematicsVector AlgebraActual

Let OA → = a → , OB → = 12 a → + 4 b → and OC → = b → , where O is the origin. If S is the parallelogram with adjacent sides OA and OC , then area of the quadrilateral OABC area of S is equal to _____

Options

  1. A6
  2. B10
  3. C7
  4. D8

Correct answer

D. 8

Step-by-step solution

Area of parallelogram, S = | a → × b → | Area of quadrilateral = Area ∆ OAB + Area ∆ OBC = 1 2 | a → × ( 12 a → + 4 b → ) | + | b → × ( 12 a → + 4 b → ) | = 1 2 | 4 a → × b → | + | 12 b → × a → | = 1 2 4 | a → × b → | + 12 | a → × b → | = 16 2 | a → × b → | = 8 | ( a → × b → ) | Ratio = 8 | ( a → × b → ) | | ( a → × b → ) | = 8

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