Three Dimensional Geometry

Let \(L_1\) (resp, \(L_2\) ) be the line passing through \(2 \hat{\mathbf{i}}-\hat{\mathbf{k}}\) (resp. \(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}})\) and parallel to \(3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}\) ( resp. \(\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) ). Then the shortest distance between the lines \(L_1\) and \(L_2\) is equal to