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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

Equation of the plane passing through the point 1 , - 1,3 , parallel to the vector i ^ + 2 j ^ + 4 k ^ and perpendicular to the plane x - 2 y + z = 6 is given by a x + b y + c z + 8 = 0 , then the value of 2 a - 5 b + 7 c is equal to

Options

  1. A32
  2. B31
  3. C- 184 5
  4. D72 5

Correct answer

C. - 184 5

Step-by-step solution

∵ required plane is passing through point 1 , - 1,3 and parallel to vector i ^ + 2 j ^ + 4 k ^ and i ^ - 2 j ^ + k ^ Therefore, the equation of plane is x - 1 y + 1 z - 3 1 2 4 1 - 2 1 = 0 ⇒ x - 1 10 - y + 1 - 3 + z - 3 - 4 = 0 ⇒ 10 x + 3 y - 4 z + 5 = 0 ⇒ 16 x + 24 5 y - 32 5 z + 8 = 0 a = 16 , b = 24 5 , c = - 32 5

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