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MHT CET2017MathematicsThree Dimensional Geometry

If the angle between the planes r → . ( m i ^ − j ^ + 2 k ^ ) + 3 = 0 and r → . ( 2 i ^ − m j ^ − i ^ ) − 5 = 0 is π 3 then m =

Options

  1. A2
  2. B± 3
  3. C3
  4. D- 2

Correct answer

C. 3

Step-by-step solution

Angle between given planes is Cos θ = n - 1 ⋅ n - 2 n - 1 n - 2 ⇒ 1 2 = 2 m + m - 2 m 2 + 5 m 2 + 5 1 2 = 3 m - 2 m 2 + 5 ⇒ m 2 + 5 = ± 6 m - 4 ⇒ m 2 + 5 = 6 m - 4 , m 2 + 5 = - 6 m + 4 m 2 - 6 m + 9 = 0 , m 2 + 6 m + 1 = 0 m - 3 2 = 0 m = 3

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