The position vectors of the vertices $$A, B$$ and $$C$$ of a tetrahedron $$ABCD$$ are $$\widehat i + \widehat j + \widehat k,\,\widehat i$$ and $$3\widehat i\,,$$ respectively. The altitude from vertex $$D$$ to the opposite face $$ABC$$ meets the median line through $$A$$ of the triangle $$ABC$$ at a point $$E.$$ If the length of the side $$AD$$ is $$4$$ and the volume of the tetrahedron is $${{2\sqrt 2 } \over 3},$$ find the position vector of the point $$E$$ for all its possible positions.