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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

If the equation of the plane passing through 1 , 2 , 3 and situated at a maximum distance from point 2 , 3 , 4 is P = 0, then the distance (in units) of P = 0 from origin is

Options

  1. A3
  2. B2 3
  3. C6
  4. D3 2

Correct answer

B. 2 3

Step-by-step solution

Let, the point A is 1 , 2 , 3 , B is 2 , 3 , 4 A B → = < 1 , 1 , 1 > Required plane must be perpendicular to A B → So, the equation of the plane is 1 x - 1 + 1 y - 2 + 1 z - 3 = 0 ⇒ x + y + z - 6 = 0 Perpendicular distance (in units) of the point 0 , 0 , 0 from the plane is 0 + 0 + 0 - 6 3 = 2 3

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