Tetrahedron \(ABCD\) has side lengths \(AB=CD=12\), and these edges are perpendicular to each other. Let \(E\) and \(F\) be the midpoints of \(AB\) and \(CD\) respectively. We are given that \(EF= 10\) and is perpendicular to both \(AB\) and \(CD\). What is the volume of \(ABCD\)?
Details and assumptions
In 3 dimensions, perpendicular lines do not need to intersect. For example, the line \(l_1 : z=0, y=0\) is perpendicular to the line \( l_2 : y=1, x=1\).