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The value of λ ∈ R such that x , y , z ≠ 0 , 0 , 0 and 2 i ^ + 3 j ^ - 4 k ^ x + 3 i ^ - j ^ + 2 k ^ y + i - 2 j ^ z = λ x i ^ + y j ^ + z k ^ lies in

Options

  1. A1 , 2
  2. B2 , 3
  3. C3 , 4
  4. D0 , 1

Correct answer

C. 3 , 4

Step-by-step solution

2 x + 3 y + z i ^ + 3 x - y - 2 z j ^ + - 4 x + 2 y k ^ = λ x i ^ + y j ^ + z k ^ Comparing both sides, we get, 2 x + 3 y + z = λ x ⇒ λ - 2 x - 3 y - z = 0 3 x - y - 2 z = λ y ⇒ - 3 x + λ + 1 y + 2 z = 0 - 4 x + 2 y = λ z ⇒ 4 x - 2 y + λ z = 0 So the system of equation has non-zero solution ⇒ λ - 2 - 3 - 1 - 3 λ + 1 2 4 - 2 λ = 0 ⇒ λ - 2 λ 2 + λ + 4 + 3 - 3 λ - 8 - 1 6 - 4 λ - 4 = 0 ⇒ λ 3 + λ 2 +

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