Example 1. As shown in the figure, points P, R, and Q are located on the edges $\mathrm{A}_{1} \mathrm{D}_{1}$, $\mathrm{C}_{1} \mathrm{C}$, and $\mathrm{BC}$ of the cube $\mathrm{ABCD}-\mathrm{A}_{1} \mathrm{~B}_{1} \mathrm{C}_{1} \mathrm{D}_{1}$, respectively. Find the trace of the plane passing through these three points on the surface of the cube.
Drawing method:
(1) Connect $QR$ and extend it to intersect $B_{1}C_{1}$ at point $H$;
(2) $\because A_{1}D_{1}$ and $B_{1}C_{1}$ are in the same plane,
$\therefore$ connect $PH$ to intersect $D_{1}C_{1}$ at point $K$,
(3) $\because K$ and $R$ are on the side face $D_{1}C$,
$\therefore$ connect $KR_{3}$
(4) Extend
$KP$ to intersect $A_{1}B_{1}$ at
$S$ point, extend $RQ$
to intersect $BB_{1}$ at $G$ point
(5) $S$,
$G$ are both on the face $A_{1}B$,
connect $SG$ to intersect
$A_{1}$ at $E$, intersect
$AB$ at $F$.
Then $F, F, Q, R, K, P$ six points are all on the three sides of $\triangle SGH$, so these six points are coplanar. Also, $E, E, Q, R, K, P$ are respectively on the surface of the cube $ABCD$-$A_{1}B_{1}C_{1}D_{1}$, so the hexagon $EFQRKP$ is the trace of the section passing through points $P, Q, R$ on the surface of the cube.