3.21. The planes $A B C_{1}$ and $A_{1} B_{1} C$ divide the triangular prism $A B C A_{1} B_{1} C_{1}$ into four parts. Find the ratio of the volumes of these parts.
3.21. Let $P$ and $Q$ be the midpoints of segments $A C_{1}$ and $B C_{1}$, i.e., $P Q$ is the line of intersection of the given planes. The ratio of the volumes of tetrahedra $C_{1} P Q C$ and $C_{1} A B C$ is $\left(C_{1} P: C_{1} A\right)\left(C_{1} Q: C_{1} B\right)=$ $=1: 4$ (see problem 3.1). It is also clear that the volume of tetrahedron $C_{1} A B C$ is $1 / 3$ of the volume of the prism. Using this, it is easy to verify that the desired ratio of volumes is $1: 3: 3: 5$.