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JEE Main202427 Jan 2024Morning ShiftMathematicsVector AlgebraActual

If a → = i ^ + 2 j ^ + k ^ , b → = 3 i ^ - j ^ + k ^ and c → be the vector such that a → × c → = b → and a → · c → = 3 , then a → · ( c → × b → - b → - c → ) is equal to

Options

  1. A32
  2. B24
  3. C20
  4. D36

Correct answer

B. 24

Step-by-step solution

Given: a → = i ^ + 2 j ^ + k ^ , b → = 3 i ^ - j ^ + k ^ , a → · c → = 3 and a → × c → = b → . Now, a → × c → = b → ⇒ a → × c → · b → = b → 2 ⇒ a → × c → · b → = 3 1 2 + 1 2 + 1 2 2 ⇒ a → × c → · b → = 27 ⇒ a → · c → × b → = 27 . . . i as a → · c → × b → = b → · a → × c → Also, a → · b → = 3 - 6 + 3 = 0 ⇒ a → · c → × b → - b → - c → = a → · c → × b → - a → · b → - a → · c → ⇒ a → · c → × b → - b → - c → = 27 - 0 - 3 ⇒ a → · c → × b → - b → - c → = 24

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