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Question

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

A
(185,5,45)
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B
(11,16,2)
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C
(12,13,14)
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D
(0,0,0)
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Solution

The correct option is A (185,5,45)
Let us assume that point (2,3,4) divides (3,2,2) and (6,17,4) in the ratio λ:1
We have 6λ+31+λ=2
λ=14
Therefore point (2,3,4) divides given two points in the ratio 1:4 externally
Let the point which divides the given two points in the ratio 1:4 internally be (x,y,z)
We have x=6+125=185 , y=1785=5 and z=4+85=45
Therefore option A is correct

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