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MHT CET202014 Oct 2020Evening ShiftMathematicsThree Dimensional GeometryActual

A A(3,2,-1) and B(1,4,3) , then equation of the plane which bisects segment AB perpendicularly

Options

  1. Ax+y+2 z+3=0
  2. Bx-y+2 z-3=0
  3. Cx+y-2 z-3=0
  4. Dx-y-2 z+3=0

Correct answer

D. x-y-2 z+3=0

Step-by-step solution

Since the plane bisects seg A B , the plane meets the line A B at the mid point i.e. ( 3+1 2 , 2+4 2 , -1+3 2 ) (2,3,1) Now line A B is er to the plane Direction ratios of plane are 1-3,4-2,3+1 i.e. -2,2,4 i.e. -1,1,2 Equation of plane passing through (2,3,1) and having d.r.s. (-1,1,2) are -(x-2)+(y-3)+2(z-1)=0 -x+2+y-3+2 z-2=0 x-y-2 z+3=0

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