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MHT CET202121 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Equation of the plane passing through the point (2,0,5) and parallel to the vectors i - j + k and 3 i +2 j + k is

Options

  1. Ax-4 y-z+3=0
  2. Bx+4 y+5 z-27=0
  3. Cx-4 y-5 z+23=0
  4. Dx-4 y+z-7=0

Correct answer

C. x-4 y-5 z+23=0

Step-by-step solution

Normal to the plane is perpendicular to the given vectors. Hence equation of normal is | array ccc i & j & k 1 & -1 & 1 3 & 2 & -1 array |= i (-1)- j (-4)+ k (5)=- i +4 j +5 k Hence equation of required plane is aligned & (-1)( x -2)+(4)( y -0)+(5)( z -5)=0 & - x +2+4 y +5 z -25=0 x -4 y -5 z +23=0 aligned

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