The sum of all values of \(\alpha\), for which the shortest distance between the lines \(\frac{x+1}{\alpha }=\frac{y−2}{…

The sum of all values of \(\alpha\), for which the shortest distance between the lines \(\frac{x+1}{\alpha }=\frac{y−2}{−1}=\frac{z−4}{−\alpha }\) and \(\frac{x}{\alpha }=\frac{y−1}{2}=\frac{z−1}{2\alpha }\) is \(\sqrt{2}\), is

[JEE Main 2026, 24 Jan (Shift 2)]