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AP EAMCET201823 Apr 2018Evening ShiftMathematicsThree Dimensional GeometryActual

The harmonic conjugate of P(-9,12,-15) with respect to the line segment A B , where A=(1,-2,3) and B=(-4,5,-6) is

Options

  1. A(- 2 3 , 1 3 , 0 )
  2. B(6,-9,12)
  3. C(- 7 3 , 8 3 ,-3 )
  4. D( 7 3 ,- 8 3 , 9 3 )

Correct answer

C. (- 7 3 , 8 3 ,-3 )

Step-by-step solution

Let point P(-9,12,-15) divides the line joining A(1,-2,3) and B(-4,5,-6) in ratio : 1 . Then, -9= -4 +1 +1 , =-2 So, harmonic conjugate of point ' P ' with respect to the line segment A B will divides the line segment A B internally in ratio 2: 1 , so point will be ( -8+1 3 , 10-2 3 , -12+3 3 )= (- 7 3 , 8 3 ,-3 )

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