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MHT CET202014 Oct 2020Evening ShiftMathematicsThree Dimensional GeometryActual

The equation of a plane passing through the intersection of two planes x+2 y-3 z+2=0 and 6 x+y+z+1=0 and parallel to the line x-1=y+2=7-z is

Options

  1. A5 x-y+4 z+1=0
  2. B5 x+y+4 z+1=0
  3. C5 x-y+4 z=1
  4. D5 x+y+4 z=1

Correct answer

C. 5 x-y+4 z=1

Step-by-step solution

Equation of plane passing through the line of intersection of given planes is (x+2 y-3 z+2)+ (6 x+y+z+1)=0(1+6 ) x+(2+ ) y+(-3+ ) z+(2+ )=0 This is parallel to the line x-1 1 = y+2 1 = z-7 -1 (1+6 )(1)+(2+ )(1)+(-3+ )(-1)=0 =-1 Hence required equation of plane is -5 x+y-4 z+1=0 5 x-y+4 z=1

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