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JEE Main202224 Jun 2022Evening ShiftMathematicsThree Dimensional GeometryActual

Let the points on the plane P be equidistant from the points - 4 , 2 , 1 and 2 , - 2 , 3 . Then the acute angle between the plane P and the plane 2 x + y + 3 z = 1 is

Options

  1. Aπ 6
  2. Bπ 4
  3. Cπ 3
  4. D5 π 12

Correct answer

C. π 3

Step-by-step solution

Plotting the diagram of the given information we get, Normal vector of plane will be = A B → = O B → - O A → = 6 i ^ - 4 j ^ + 2 k ^ = 2 3 i ^ - 2 j ^ + k ^ Now equation of plane is given by, P ≡ 3 x + 1 - 2 y + 1 z - 2 = 0 P ≡ 3 x - 2 y + z + 1 = 0 Assuming other plane to be P ' ≡ 2 x + y + 3 z - 1 = 0 Now the angle between them is given by, cos θ = n ^ 1 · n ^ 2 n 1 n 2 θ = cos - 1 6 - 2 + 3 14 × 14 θ = cos - 1 7 14 = = cos - 1 1 2 = π 3

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