Let P (α, β, γ) be the point on the line (x-1)/2=(y+1)/-3=z at a distance 4 √ 14 from the point (1,-1,0) and nearer to the origin. Then the shortest…

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