$12.2 .1 *$ As shown in the figure, for the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, a line $l$ is drawn 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
Obviously, $A D_{1} // B C_{1}$, the number of lines passing through point $A$ that form a $60^{\circ}$ angle with both lines $A C$ and $A D_{1}$ is 3. Therefore, the number of lines $l$ passing through point $A_{1}$ that satisfy the conditions is also 3. Hence, the answer is C.