The position vectors of the vertices A, B, C of a tetrahedron ABCD are \(\hat{i} + \hat{j} + \hat{k}\), \(\hat{i}\) and \(3\hat{i}\) respectively and the altitude from the vertex D to the opposite face ABC meets the face at E. If the volume of the tetrahedron is \(\dfrac{2\sqrt{2}}{3}\), then the length of DE is: