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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

A plane P 1 has the equation 4 x - 2 y + 2 z = 3 and P 2 has the equation - x + k y - 2 z = 7 . If the angle between P 1 and P 2 is 2 π 3 , then the value of k can be

Options

  1. A1
  2. B2
  3. C- 17
  4. D17

Correct answer

D. 17

Step-by-step solution

A normal vector to plane P 1 is < 2 , - 1 , 1 > A normal vector to plane P 2 is < - 1 , k , - 2 > Now, cos ⁡ 2 π 3 = - 2 - k - 2 6 k 2 + 5 = - 1 2 ⇒ 2 k + 4 2 = 6 k 2 + 30 ⇒ 4 k 2 + 32 k + 64 = 6 k 2 + 30 ⇒ 2 k 2 - 32 k - 34 = 0 ⇒ k 2 - 16 k - 17 = 0 ⇒ k - 17 k + 1 = 0 ⇒ k = 17 , - 1

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