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BITSAT2014MathematicsThree Dimensional GeometryActual

The equation of the right bisector plane of the segment joining (2,3,4) and (6,7,8) is

Options

  1. Ax+y+z+15=0
  2. Bx+y+z-15=0
  3. Cx-y+z-15=0
  4. DNone of these

Correct answer

B. x+y+z-15=0

Step-by-step solution

If the given points be A(2,3,4) and B(6,7,8), then their mid-point N (4,5,6) must lie on the plane. The direction ratios of AB are 4,4,4, i.e. 1,1,1 The required plane passes through N (4,5,6) and is normal to AB . Thus its equation is 1(x-4)+1(y-5)+1(z-6)=0 x+y+z=15

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