3.23. In what ratio does a plane divide the volume of a tetrahedron if the plane is parallel to two of its skew edges and divides one of the other edges in the ratio $2: 1?$
3.23. The section of the tetrahedron by a given plane is a parallelogram. Each of the two resulting parts of the tetrahedron can be cut into a pyramid, the base of which is this parallelogram, and a tetrahedron. The volumes of these pyramids and tetrahedrons can be expressed in terms of the lengths $a$ and $b$ of the intersecting edges, the distance $d$, and the angle $\varphi$ between them (for the tetrahedrons, use the formula from problem 3.4). Thus, the volumes of the resulting parts are found; they are $10 v / 81$ and $7 v / 162$, where $v = a b d \sin \varphi$, and their ratio is $20 / 7$.