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MHT CET202120 Sep 2021Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of the plane that contains the line of intersection of the planes. x+2 y+3 z-4=0 and 2 x+y+5=0 and is perpendicular to the plane 5 x+3 y-6 z+8=0 is

Options

  1. A14 x+7 y-7 z-4=0
  2. B33 x+45 y+50 z-41=0
  3. C-33 x +45-50 z +41=0
  4. D5 x+31 y+50 z-41=0

Correct answer

B. 33 x+45 y+50 z-41=0

Step-by-step solution

The equation of the required plane is (x+2 y+3 z-4)+ aligned & (2 x+y-z+5)=0 i.e. & (1+2 ) x+(2+ ) y+(3- ) z+(-4+5 )=0 aligned Since (1) is perpendicular to the plane 5 x+3 y-6 z+8=0 , we write aligned & (1+2 )(5)+(2+ )(3)+(3- )(-6)=0 & 5+10 +6+3 -18+6 =0 & 19 =7 & = 7 19 aligned Substituting value of in eq. (1), we get aligned & (1+ 14 19 ) x + (2+ 7 19 ) y + (3- 7 19 ) z + (-4+ 35 19 )=0 & 33 x +45 y +50 z -41=0 aligned

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