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JEE Main202227 Jul 2022Morning ShiftMathematicsVector AlgebraActual

Let a → = 2 i ^ - j ^ + 5 k ^ and b → = α i ^ + β j ^ + 2 k ^ . If a → × b → × i ^ · k ^ = 23 2 , then b → × 2 j ^ is equal to

Options

  1. A4
  2. B5
  3. C21
  4. D17

Correct answer

B. 5

Step-by-step solution

Given, a → = 2 i ^ - j ^ + 5 k ^ , b → = α i ^ + β j ^ + 2 k ^ Also given a → × b → × i ^ · k ^ = 23 2 , then b → × 2 j ^ is Now using triple cross product we have, a → · i ^ b → - b → · i ^ a → · k ^ = 23 2 ⇒ 2 . b → - α · a → . k ^ = 23 2 ⇒ 2 × 2 - α × 5 = 23 2 ⇒ 5 α = 4 - 23 2 ⇒ α = - 3 2 Now finding, b → × 2 j ^ = i ^ j ^ k ^ α

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