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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

If the angle between the plane x - 3 y + 2 z = 1 and the line x - 1 2 = y - 1 - 1 = z - 1 - 3 is θ , then sec ⁡ 2 θ is equal to

Options

  1. A107 11
  2. B98 97
  3. C100 9
  4. D87 79

Correct answer

B. 98 97

Step-by-step solution

A normal vector to the plane n → = < 1 , - 3 , 2 > A vector parallel to the line b → = < 2 , - 1 , - 3 > sin θ = b → . n → b → ⋅ n → = 2 + 3 − 6 14 14 = − 1 14 sec ⁡ 2 θ = 1 cos ⁡ 2 θ = 1 1 - 2 s i n 2 θ = 1 1 - 2 196 = 196 194 = 98 97

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