Let \( P(\alpha, \beta, \gamma) \) 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:
