3. As shown in Figure 1, for the cube $A B C D-$ $A_{1} B_{1} C_{1} D_{1}$, draw a line $l$ through vertex $A_{1}$ such that $l$ forms an angle of $60^{\circ}$ with both lines $A C$ and $B C_{1}$. How many such lines $l$ are there?
(A) 1
(B) 2
(C) 3
(D) More than 3
3.C.

Obviously, $A D_{1} // B C_{1}$. There are 3 lines passing through point $A$ that form a $60^{\circ}$ angle with both lines $A C$ and $A D_{1}$. Therefore, there are also 3 lines $l$ passing through point $A_{1}$ that satisfy the conditions.