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AP EAMCET2016MathematicsStraight Lines

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

Options

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

Correct answer

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

Step-by-step solution

Let we points P (2,3,4), A (3,-2,2) and B (6,-17,-4) . and P divides AB in the ratio k: 1 then aligned & (2,3,4)= ( 6 k+3 k+1 , -17 k-2 k+1 , -4 k+2 k+1 ) & 2= 6 k+3 k+1 & 2 k+2=6 k+3 & -4 k=1 k=- 1 4 aligned Harmonic conjugate Q divides in the ratio -k: 1 , So Ratio will be 1 4 : 1 Coordinates of 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 ,-5 4 5 ) aligned

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