Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

The shortest distance between the lines is $SD=\frac{\left|\begin{array}{ccc}1& 2& 2\\ 2& 3& 4\\ 3& 2& 5\end{array}\right|}{|(2,3,4)\times (3,2,5)|}=\frac{1}{\sqrt{78}}$

 

. Any distance $d$ between a point on each line satisfies $d\ge \frac{1}{\sqrt{78}}$, so its reciprocal satisfies $0<\frac{1}{d}\le \sqrt{78}\approx 8.83$. Hence the reciprocal can be less than 9, has no minimum value, can equal $2\sqrt{19}=\sqrt{76}$, and cannot be greater than 78.