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AP EAMCET20224 Jul 2022Evening ShiftMathematicsThree Dimensional GeometryActual

If the equation of the plane which is at a distance of 1 3 units from the origin and perpendicular to a line whose directional ratios are 1 , 2 , 2 is x + p y + q z + r = 0 then p 2 + q 2 + r 2 =

Options

  1. A3
  2. B5
  3. C13
  4. D2

Correct answer

A. 3

Step-by-step solution

Given, Direction ratio of perpendicular line to the plane is 1 , 2 , 2 , So the equation of the plane will be x + 2 y + 2 z = d Now given distance from origin is 1 3 , So by perpendicular distance formula we get, d 1 2 + 2 2 + 2 2 = 1 3 ⇒ d = 1 So, equation of plane will be x + 2 y + 2 z - 1 = 0 Now comparing equation of plane with x + p y + q z + r = 0 We get, p = 2 ,   q = 2   &   r = - 1 So, the value of p 2 + q 2 + r 2 = 2 2 + 2 2 + 1 2 = 9 = 3

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