Let \(\text{P}\left(\alpha ,\beta ,\gamma \right)\) be the point on the line \(\frac{x−1}{2}=\frac{y+1}{−3}=z\) at a dis…

Let \(\text{P}\left(\alpha ,\beta ,\gamma \right)\) be the point on the line \(\frac{x−1}{2}=\frac{y+1}{−3}=z\) at a distance \(4\sqrt{14}\) from the point \((1, –1, 0)\) and nearer to the origin. Then the shortest distance, between the lines \(\frac{x−\alpha }{1}=\frac{y−\beta }{2}=\frac{z−\gamma }{3}\) and \(\frac{x+5}{2}=\frac{y−10}{1}=\frac{z−3}{1}\), is equal to

[JEE Main 2026, 22 Jan (Shift 1)]