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JEE Main202312 Apr 2023Morning ShiftMathematicsVector AlgebraActual

Let λ ∈ ℤ , a → = λ i ^ + j ^ - k ^ and b → = 3 i ^ - j ^ + 2 k ^ . Let c → be a vector such that a → + b → + c → × c → = 0 → , a → · c → = - 17 and b → · c → = - 20 . Then c → × λ i ^ + j ^ + k ^ 2 is equal to

Options

  1. A46
  2. B53
  3. C62
  4. D49

Correct answer

A. 46

Step-by-step solution

Given that a → = λ i ^ + j ^ - k ^ b → = 3 i ^ - j ^ + 2 k ^ Also a → + b → + c → × c → = 0 → ⇒ k a → + b → = c → a → · c → = - 17 and b → · c → = - 20 Now, Take a → · c → = - 17 ⇒ k λ i ^ + j ^ - k ^ · λ i ^ + j ^ - k ^ + 3 i ^ - j ^ + 2 k ^ = - 17 ⇒ k λ 2 + 3 λ + 0 - 1 = - 17 ⇒ k λ 2 + 3 λ - 1 = - 17   . . . . ( 1 ) Similarly, on t

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