3. Let the hyperbola $C: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1, A_{1} 、 A_{2}$ be the left and right vertices of the hyperbola $C$, and $F$ be a focus of $C$. A circle centered at the origin $O$ with radius $|O F|$ intersects one of the asymptotes of $C$ at point $B$. If $\angle A_{1} B A_{2}=60^{\circ}$, then the eccentricity of $C$ is $\qquad$
3. $\frac{\sqrt{21}}{3}$.

Let's take the intersection point $B$ in the first quadrant, it is easy to know that $B(a, b)$. Then $\tan 60^{\circ}=\frac{2 a}{b} \Leftrightarrow 4 a^{2}=3 b^{2}$
$$
\begin{array}{l}
\Rightarrow 4 a^{2}=3\left(c^{2}-a^{2}\right) \\
\Leftrightarrow e^{2}=\frac{7}{3} \Leftrightarrow e=\frac{\sqrt{21}}{3} .
\end{array}
$$