3. As shown in Figure 1, given a cube $A B C D$ $A_{1} B_{1} C_{1} D_{1}$, draw a line $l$ through vertex $A_{1}$ in space such that $l$ forms an angle of $60^{\circ}$ with both lines $A C$ and $B C_{1}$. How many such lines $l$ can be drawn?
(A) 4
(B) 3
(C) 2
(D) 1
3. (B).

It is easy to know that the angle formed by the skew lines $A C$ and $B C_{1}$ is $60^{\circ}$, so this problem is equivalent to:

Given that the angle formed by the skew lines $a$ and $b$ is $60^{\circ}$, how many lines pass through a fixed point $P$ in space and form an angle of $60^{\circ}$ with both $a$ and $b$?

This is similar to a multiple-choice question from the 1993 National College Entrance Examination in Mathematics, and it is not difficult to determine that there should be 3 lines.