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The number of distinct real values of λ , for which the lines x - 1 1 = y - 2 2 = z + 3 λ 2 and x - 3 1 = y - 2 λ 2 = z - 1 2 , are coplanar is

Options

  1. A2
  2. B4
  3. C3
  4. D1

Correct answer

C. 3

Step-by-step solution

∵ Lines are coplanar ∴ 3 - 1 2 - 2 1 - - 3 1 2 λ 2 1 λ 2 2 = 0 ⇒ 2 0 4 1 2 λ 2 1 λ 2 2 = 0 ⇒ 2 4 - λ 4 + 4 λ 2 - 2 = 0 ⇒ 4 - λ 4 + 2 λ 2 - 4 = 0 ⇒ λ 2 λ 2 - 2 = 0 ⇒ λ = 0 ,   2 ,   - 2

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