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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

Let L 1 be the projection and L 2 be the image of z -axis in the plane 3 x - 4 y + z + 1 = 0 . The distance of the point 1,2 , 3 from the plane containing the lines L 1 and L 2 is

Options

  1. A2 units
  2. B4 units
  3. C5 units
  4. D6 units

Correct answer

A. 2 units

Step-by-step solution

The required plane must contain z -axis and parallel to normal vector of the given plane A parallel vector to z -axis is < 0,0 , 1 > Normal vector to the given plane is < 3 , - 4,1 > A normal vector to the required plane = i ^ j ^ k ^ 0 0 1 3 - 4 1 = 4 i ^ + 3 j ^ ∵ Required plane contain z axis, so it must pass through 0,0 , 0 Equation of the required plane is 4 x - 0 + 3 y - 0 = 0 ⇒ 4 x + 3 y = 0 So, the perpendicular distance from 1,2 , 3 to 4 x + 3 y = 0 is 4 + 6 5 = 2 units

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