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JEE Main202126 Aug 2021Morning ShiftMathematicsVector AlgebraActual

Let a → = i ^ + j ^ + k ^ and b → = j ^ - k ^ . If c → is a vector such that a → × c → = b → and a → · c → = 3 , then a → · ( b → × c → ) is equal to:

Options

  1. A6
  2. B- 2
  3. C2
  4. D- 6

Correct answer

B. - 2

Step-by-step solution

We know that, for vectors a → ,   b → and c → a → · ( b → × c → ) = a → b → c → = c → a → b → ⇒ a → · ( b → × c → ) = ( c → × a → ) · b → = - b → · b → ∵ a → × c → = b → ⇒ c → × a → = - b → = - b → 2 = - 1 2 + - 1 2 2 = - 2

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