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If the planes r → ⋅ i ^ + j ^ + k ^ = 1 , r → ⋅ i ^ + 2 a j ^ + k ^ = 2 and r → ⋅ a i ^ + a 2 j ^ + k ^ = 3 intersect in a line, then the possible number of real values of a is

Options

  1. A1
  2. B2
  3. C4
  4. D0

Correct answer

D. 0

Step-by-step solution

∵ all 3 planes intersect in a line ⇒ 1 1 1 1 2 a 1 a a 2 1 = 0 ⇒ 2 a - a 2 - 1 1 - a + 1 a 2 - 2 a 2 = 0 ⇒ 2 a - a 2 - 1 + a - a 2 = 0 ⇒ - 2 a 2 + 3 a - 1 = 0 ⇒ a = 1 , 1 2 for both values of a = 1 , 1 2 , two of the given 3 planes are parallel (rejected)

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