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BITSAT 2014
Exam
BITSAT
Year
2014
Subject
Mathematics
Chapter
Three Dimensional Geometry

BITSAT 2014 · Mathematics · Three Dimensional Geometry

The equation of the right bisector plane of the segment joining...

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

Options

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

Correct answer

B. x+y+z−15=0x+y+z-15=0

Step-by-step solution

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