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JEE Main202325 Jan 2023Morning ShiftMathematicsVector AlgebraActual

Let a → , b → and c → be three non zero vectors such that b → · c → = 0 and a → × ( b → × c → ) = b → - c → 2 . If d → be a vector such that b → · d → = a → · b → , then ( a → × b → ) · ( c → × d → ) is equal to

Options

  1. A3 4
  2. B1 2
  3. C- 1 4
  4. D1 4

Correct answer

D. 1 4

Step-by-step solution

Given, a → × b → × c → = b → - c → 2 Using the vector triple cross product we have, a → × b → × c → = a → · c → b → - a → · b → c → So, ( a → · c → ) b → - ( a → · b → ) c → = b → - c → 2 On comparing both sides we get, a → · c → = 1 2 , a → · b → = 1 2 ∵   b → · d →   =   a

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