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JEE Main202313 Apr 2023Morning ShiftMathematicsVector AlgebraActual

Let a → = i ^ + 4 j ^ + 2 k ^ , b → = 3 i ^ - 2 j ^ + 7 k ^ and c → = 2 i ^ - j ^ + 4 k ^ . If a vector d → satisfies d → × b → = c → × b → and d → · a → = 24 , then d → 2 is equal to

Options

  1. A323
  2. B423
  3. C313
  4. D413

Correct answer

D. 413

Step-by-step solution

We have been given that d → × b → = c → × b → ⇒ ( d → - c → ) × b → = 0 ⇒ d → - c → = λ b →    ( ∵ d → ≠ c → ) ⇒ d → = c → + λ b → It is given that a → · d → = 24 ⇒ a → · c → + λ b → · a → = 24 ⇒ 6 + λ ( 3 - 8 + 14 ) = 24 ⇒ 9 λ = 18 ⇒ λ = 2 ∴ d → = c →

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