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MHT CET20244 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

A plane which is perpendicular to two planes 2 x-2 y+z=0 and x-y+2 z=4 , passes through (1,-2,1) . The distance of the plane from the point (1,2,2) is

Options

  1. A0 units
  2. B1 units
  3. C2 units
  4. D2 2 units

Correct answer

D. 2 2 units

Step-by-step solution

The equation of a plane passing through (1,-2,1) is a (x-1)+ b (y+2)+ c ( z -1)=0...(i) aligned & Plane (i) is perpendicular to planes & 2 x-2 y+z=0 and x-y+2 z=4 . & array l 2 a-2 b+c=0, and ...(i) a-b+2 c=0 ...(ii) Solving (ii) and (iii), we get a=-3, b=-3, c=0 array aligned Substituting the values of a, b, c in equation (i), we get x+y+1=0 The distance of this plane from (1,2,2) is d= | 1+2+1 1+1 |=2 2

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