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JEE Main2015MathematicsVector AlgebraActual

In a parallelogram A B C D , A B → = a , A D → = b & A C → = c . D B → · A B → has the value:

Options

  1. A1 2 a 2 + b 2 + c 2
  2. B1 4 a 2 + b 2 - c 2
  3. C1 3 b 2 + c 2 - a 2
  4. D1 2 a 2 - b 2 + c 2

Correct answer

D. 1 2 a 2 - b 2 + c 2

Step-by-step solution

A B → = a A D → = b A C → = b → + a → = c Squaring both side b → 2 + a → 2 - 2 b → · a → = c 2 b 2 + a 2 - c 2 = 2 b → · a → … 1 D B → . A B → = a → - b → · a → = a → 2 - a → · b → = 1 2 ( a 2 - b 2 + c 2 )

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