Example 6 (1997 National High School League Question) If three lines $a$, $b$, and $c$ in space are pairwise skew lines, then the number of lines that intersect $a$, $b$, and $c$ is ( ).
A. 0 lines
B. 1 line
C. More than 1 but a finite number of lines
D. Infinitely many lines
Solution: Choose D. Reason: First, regardless of the positions of $a$, $b$, and $c$, a parallelepiped $A B C D-A_{1} B_{1} C_{1} D_{1}$ can always be constructed such that $A B$ lies on line $a$, $B_{1} C_{1}$ lies on line $b$, and $D_{1} D$ lies on line $c$, as shown in Figure 7-6. Next, take any point $M$ on the extension of $D D_{1}$, and determine a plane $\alpha$ with $M$ and $a$. Plane $\alpha$ intersects line $B_{1} C_{1}$ at $P$ and line $A_{1} D_{1}$ at $Q$, so $P Q / / \alpha$. Therefore, within plane $\alpha$, line $P M$ does not parallel $\alpha$, and $P M$ must intersect $\alpha$ at a point $N$. Thus, line $M N$ intersects lines $a$, $b$, and $c$ simultaneously. Since there are infinitely many ways to choose point $M$, there are infinitely many lines that intersect $a$, $b$, and $c$ simultaneously.