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JEE Main201912 Apr 2019Evening ShiftMathematicsVector AlgebraActual

Let α   ∈ R and the three vectors a → = α i ^ + j ^ + 3 k ^ ,    b → = 2 i ^ + j ^ - α k ^ and c → = α i ^ - 2 j ^ + 3 k ^ . Then the set S = α : a → , b → and c → are coplanar

Options

  1. Ais singleton
  2. Bcontains exactly two positive numbers
  3. Cis empty
  4. Dcontains exactly two numbers only one of which is positive

Correct answer

C. is empty

Step-by-step solution

If a → ,   b →   and   c → are coplanar then, α 1 3 2 1 - α α - 2 3 = 0 ⇒ 3 α 2 + 18 = 0 ⇒ α ∈ ϕ

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