The shortest distance between the lines r =(1/3 i +2 j +8/3 k )+λ(2 i -5 j +6 k ) and r =(-2/3 i -1/3 k )+μ( j - k ), λ, μ ∈ R, is:

The shortest distance between the lines $$\begin{aligned} & \vec{r}=\left(\frac{1}{3} \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+\frac{8}{3} \hat{\mathrm{k}}\right)+\lambda(2 \hat{\mathrm{i}}-5 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}) \\ & \text { and } \vec{r}=\left(-\frac{2}{3} \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{k}}\right)+\mu(\hat{\mathrm{j}}-\hat{\mathrm{k}}), \lambda, \mu \in \mathbb{R}, \text { is: } \end{aligned} $$