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AP EAMCET202022 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane mid-parallel to the planes 2 x-3 y+6 z+21=0 and 2 x-3 y+6 z-14=0 is given by

Options

  1. A4 x+6 y-12 z+7=0
  2. B4 x-6 y-12 z-7=0
  3. C4 x-6 y+12 z+7=0
  4. D4 x+6 y+12 z-7=0

Correct answer

C. 4 x-6 y+12 z+7=0

Step-by-step solution

Let equation of plane 2 x-3 y+6 z+d=0 is equidistance from two parallel planes 2 x-3 y+6 z+21=0 and 2 x-3 y+6 z-14=0 So, |21-d| 4+9+36 = |d+14| 4+9+36 21-d=d+14 2 d=7 d= 7 2 Equation of required plane is 4 x-6 y+12 z+7=0

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