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AP EAMCET202124 Aug 2021Morning ShiftMathematicsStraight LinesActual

The harmonic conjugate of the point (2,3,4) with respect to the point (3,-2,2) and (6,-17,-4) is

Options

  1. A( 18 5 ,-5, 4 5 )
  2. B(11,-16,2)
  3. C( 1 2 , 1 3 , 1 4 )
  4. D(0,0,0)

Correct answer

A. ( 18 5 ,-5, 4 5 )

Step-by-step solution

Given, Let P(2,3,4), A(3,-2,2) and B(6,-17,-4) are three points. Let P divides A B in the ratios : 1 , then aligned 2 & = 6 +3 +1 2 +2 & =6 +3 2-3 & =6 -2 & =- 1 4 aligned Harmonic conjugate Q divides in the ratio - : 1 i.e. 1 4 : 1 . Coordinate of point Q . aligned & = [ 1 4 (6)+3 1 4 +1 , 1 4 (-17)-2 1 4 +1 , 1 4 (-4)+2 1 4 +1 ] & = ( 6+12 5 , -17-8 5 , -4+8 5 ) & = ( 18 5 ,- 25 5 , 4 5 ) & = ( 18 5 ,-5, 4 5 ) aligned

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