Example 2. In the quadrilateral pyramid $\mathrm{S}-\mathrm{ABCD}$, $\mathrm{ABCD}$ is a rectangle, $\mathrm{AB}=\sqrt{2} \mathrm{a}, \mathrm{BC}=\mathrm{a}, \mathrm{AC} \cap \mathrm{BD}=$ $\mathrm{O}, \mathrm{SO} \perp$ plane $\mathrm{ABCD}$, and $\mathrm{SO}=\frac{\mathrm{a}}{2}$, find the distance between $\mathrm{AC}$ and $\mathrm{SB}$.
As shown in Figure 3, the dihedral angle $\mathrm{S}-\mathrm{AC}-\mathrm{B}$ has a plane angle of $90^{\circ}$, the distance from $\mathrm{S}$ to $\mathrm{AC}$ is $\mathrm{SO} = \frac{\mathrm{a}}{2}$, and the distance from $\mathrm{B}$ to $\mathrm{AC}$ is

From formula (2), the distance $\mathrm{h}$ between the skew lines $\mathrm{AC}$ and $\mathrm{SB}$ is $\mathrm{h} = \frac{\sqrt{22}}{11} \mathrm{a}$.