The shortest distance between the lines \(l_{1}\) and \(l_{2}\) whose vector equations are \(\vec{r}=\hat{i}+\hat{j}+\lambda(2\hat{i}-\hat{j}+\hat{k})\) and \(\vec{r}=2\hat{i}+\hat{j}-\hat{k}+\mu(3\hat{i}-5\hat{j}+2\hat{k})\) is

\(\frac{10}{\sqrt{59}}\)

\(d=\left|\frac{(\vec{b_{1}}\times \vec{b_{2}})\cdot (\vec{a_{2}}-\vec{a_{1}})}{|\vec{b_{1}}\times \vec{b_{2}}|}\right|\)