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JEE Main202228 Jun 2022Morning ShiftMathematicsThree Dimensional GeometryActual

The acute angle between the planes P 1 and P 2 , when P 1 and P 2 are the planes passing through the intersection of the planes 5 x + 8 y + 13 z - 29 = 0 and 8 x - 7 y + z - 20 = 0 and the points 2 , 1 , 3 and 0 , 1 , 2 , respectively, is

Options

  1. Aπ 3
  2. Bπ 4
  3. Cπ 6
  4. Dπ 12

Correct answer

A. π 3

Step-by-step solution

Equation of plane passing through the intersection of two planes 5 x + 8 y + 13 z - 29 = 0 and 8 x - 7 y + z - 20 = 0 can be written as 5 x + 8 y + 13 z - 29 + λ 8 x - 7 y + z - 20 = 0 and if it is passing through 2 , 1 , 3 then 10 + 8 + 39 - 29 + λ 16 - 7 + 3 - 20 = 0 i.e. λ = 7 2 . P 1 : Equation of plane through intersection of 5 x + 8 y + 13 z - 29 = 0 and 8 x - 7 y + z - 20 = 0 and the point 2 , 1 , 3 is 5 x + 8 y + 13 z - 29 + 7 2 8 x - 7 y + z - 20 = 0 ⇒ 2 x - y + z = 6 Similarly P 2 : E

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