Example 1. In a tetrahedron $ABCD$ with all edges of equal length, $E, F$ are the midpoints of edges $AD, BC$ respectively. Connect $AF, CE$. Find the size of the angle formed by the skew lines $AF$ and $CE$.
Solve As shown in Figure 16-1, connect $D F$, take the midpoint $G$ of $D F$, and connect $G E$, then $E G / / A F$, so $\angle G E C$ is the angle formed by the skew lines $A F$ and $C E$.
Assume the edge length of the tetrahedron is $a$, then $A F=C E=\frac{\sqrt{3}}{2} a, E G=\frac{1}{2} A F=\frac{\sqrt{3}}{4} a$
Connect $G C$, then $G C=\sqrt{F G^{2}+F C^{2}}=\sqrt{\frac{a^{2}}{4}+\frac{3 a^{2}}{16}}=\frac{\sqrt{7} a}{4}$
By the cosine rule, we get $\cos \angle G E C=\frac{E G^{2}+C E^{2}-G C^{2}}{2 E G \cdot C E}=\frac{2}{3}$
Therefore, $\angle G E C=\arccos \frac{2}{3}$, that is, the angle formed by the skew lines $A F$ and $C E$ is $\arccos \frac{2}{3}$.