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MHT CET20242 May 2024Morning ShiftMathematicsThree Dimensional GeometryActual

The Cartesian equation of the plane, passing through the points (3,1,1),(1,2,3) and (-1,4,2) , is

Options

  1. A5 x+6 y-2 z-23=0
  2. B-5 x+6 y+2 z+23=0
  3. C5 x+6 y+2 z-23=0
  4. D5 x-6 y+2 z-23 0

Correct answer

C. 5 x+6 y+2 z-23=0

Step-by-step solution

Equation of plane passing through (3,1,1) , (1,2,3) and (-1,4,2) is aligned & | array ccc x-3 & y-1 & z-1 1-3 & 2-1 & 3-1 -1-3 & 4-1 & 2-1 array |=0 & | array ccc x-3 & y-1 & z-1 -2 & 1 & 2 -4 & 3 & 1 array |=0 & (x-3)(1-6)-(y-1)(-2+8) +(z-1)(-6+4)=0 & -5(x-3)-6(y-1)-2(z-1)=0 & -5 x+15-6 y+6-2 z+2=0 . & -5 x-6 y-2 z +23=0 & 5 x+6 y+2 z-23=0 aligned

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