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AP EAMCET201823 Apr 2018Evening ShiftMathematicsThree Dimensional GeometryActual

If the equation of the plane bisecting the line segment joining the points P(3,2,4) and Q(-1,0,-2) and perpendicular to P Q is a x+b y+c z+d=0 , then a c+b d

Options

  1. A0
  2. B12
  3. C6
  4. D1

Correct answer

A. 0

Step-by-step solution

Mid-point of line segment joining the points P(3,2,4) and Q(-1,0,-2) is R(1,1,1) and direction ratios of line segment P Q is 4,2,6 , so direction ratios of normal to the plane is a, b, c = 4,2,6 . So, equation of plane will be 4 x+2 y+6 z+d=0 Since, plane (i) bisect the line segment joining P Q . So, d=-12 Therefore, a c+b d=0 .

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