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MHT CET20239 May 2023Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of a plane, containing the line of intersection of the planes 2 x-y-4=0 and y+2 z-4=0 and passing through the point (2,1,0) , is

Options

  1. A3 x-2 y+z=4
  2. B3 x+2 y+z=4
  3. C3 x-2 y-z=4
  4. D3 x+2 y-z=-4

Correct answer

C. 3 x-2 y-z=4

Step-by-step solution

Equation of plane passing through the intersection of given planes is 2 x-y-4+ (y+2 z-4)=0 Since, the plane passes through (2,1,0) aligned & 2(2)-1-4+ (1+2(0)-4)=0 & 4-1-4-3 =0 & -1-3 =0 & = -1 3 aligned Substituting = -1 3 in equation (i), we get aligned & 2 x-y-4- 1 3 (y+2 z-4)=0 & 6 x-3 y-12-y-2 z+4=0 & 6 x-4 y-2 z-8=0 & 3 x-2 y-z=4 aligned

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