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