设异面直线 $a,b$ 成 $\alpha$ 角，且 $\alpha\in\left(0,\dfrac{\pi}{2}\right]$，$A$ 为空间一点，且过 $A$ 与 $a,b$ 都成 $\theta$ 角的直线条数：$$\begin{array}{|c|c|c|c|c|c|c|}\hline \theta &0\leqslant\theta<\dfrac{\alpha}{2} &\theta=\dfrac{\alpha}{2} &\dfrac{\alpha}{2}<\theta<\dfrac{\pi-\alpha}{2} &\theta=\dfrac{\pi-\alpha}{2} &\dfrac{\pi-\alpha}{2}<\theta<\dfrac{\pi}{2} & \theta=\dfrac{\pi}{2}\\ \hline \text{条数}&0 &1&2 &3 &4 &1\\ \hline\end{array}$$如图，$BC_1$ 与 $AC$ 成 $60^\circ$，所以满足条件的直线 $l$ 有 $3$ 条．