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The harmonic conjugate of $P (5, 4, - 6)$ divides the line segment joining the points $A (3, 2, - 4)$ and $B (9, 8, - 10)$ is

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$(- 5, 4, 6)$

$(5, - 4, - 6)$

$(- 3, - 4, 2)$

answer is B.

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Detailed Solution

P divides A, B in the ratio $3 - 5 : 5 - 9 = 1 : 2$
$Q =$ Harmonic Conjugate of P divides A,B in the ratio $1 : 2$ externally
$∴ Q = \frac{B - 2 A}{1 - 2} = (- 3, - 4, 2)$

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