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MHT CET20243 May 2024Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2 x-y-2 z=5 and 3 x-6 y+2 z=7 is

Options

  1. A14 x+10 y+9 z =13
  2. B14 x+10 y+9 z=33
  3. C14 x+10 y+9 z=-15
  4. D14 x+10 y+9 z=-33

Correct answer

D. 14 x+10 y+9 z=-33

Step-by-step solution

Required plane is perpendicular to planes 2 x-y-2 z=5 and 3 x-6 y+2 z=7 Equation of required plane is aligned & | array ccc x-1 & y-1 & z-1 2 & -1 & -2 3 & -6 & 2 array |=0 & (x-1)(-14) (y-1)(10) & +(z-1)(-12+3)=0 & -14 x+14-10 y+10-9 z+9=0 & 14 x+10 y+9 z=-33 aligned

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