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JEE Main202331 Jan 2023Evening ShiftMathematicsThree Dimensional GeometryActual

Let P be the plane, passing through the point 1 , - 1 , - 5 and perpendicular to the line joining the points 4 , 1 , - 3 and 2 , 4 , 3 . Then the distance of P from the point 3 , - 2 , 2 is

Options

  1. A6
  2. B4
  3. C5
  4. D7

Correct answer

C. 5

Step-by-step solution

Given, P be the plane, passing through the point 1 , - 1 , - 5 and perpendicular to the line joining the points 4 , 1 , - 3 and 2 , 4 , 3 , So, direction ratio of Plane Normal will be, 4 - 2 , 1 - 4 , - 3 - 3 ≡ 2 , - 3 , - 6 Now, equation of Plane will be, 2 x - 1 - 3 y + 1 - 6 z + 5 = 0 ⇒ 2 x - 3 y - 6 z - 35 = 0 Hence, perpendicular distance of plane from 3 , - 2 , 2 will be, Distance = 2 × 3 - 3 × - 2 - 6 × 2 - 35 2 2 + - 3 2 + - 6 2 = 6 + 6 - 12 - 35 2 2 + - 3 2 + - 6 2 = 5 .

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