The reciprocal of the distance between two points, one on each of the lines $\frac{x - 2}{3} = \frac{y - 4}{2} = \frac{z - 5}{5}$ and $\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}$

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is having minimum value $5 \sqrt{3}$

Cannot be greater than 78

Cannot be less than 9

Cannot be $2 \sqrt{19}$

answer is D.

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Detailed Solution

The shortest distance (SD) =

$\frac{|\begin{array}{ccc} 21 & 4 - 2 & 5 - 3 \\ 2 & 3 & 4 \\ 3 & 2 & 5 \end{array}|}{|\begin{array}{ccc} i & j & k \\ 2 & 3 & 4 \\ 3 & 2 & 5 \end{array}|} = \frac{1}{\sqrt{78}} So, \frac{1}{S D} = \sqrt{78}$

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