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JEE Main201912 Jan 2019Evening ShiftMathematicsThree Dimensional GeometryActual

If an angle between the line, x + 1 2 = y - 2 1 = z - 3 - 2 and the plane, x - 2 y - k z = 3 is cos - 1 2 2 3 , then a value of k is

Options

  1. A5 3
  2. B3 5
  3. C- 3 5
  4. D- 5 3

Correct answer

A. 5 3

Step-by-step solution

cos 90 - θ = n → 1 . v → n 1 → v → ⇒ s i n θ = i ^ - 2 j ^ - k k ^ . 2 i ^ + j ^ - 2 k ^ 1 + 4 + k 2 4 + 1 + 4 ∵ θ = cos - 1 2 2 3 ⇒ cos θ = 2 2 3 ⇒ sin θ = 1 3 ⇒ 1 3 = 2 - 2 + 2 k 3 5 + k 2 2 k = 5 + k 2 ⇒ k = ± 5 3

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