3. In $\triangle A B C$, it is known that the angle between $\overrightarrow{A B}$ and $\overrightarrow{B C}$ is $150^{\circ},|\overrightarrow{A C}|=2$. Then the range of $|\overrightarrow{A B}|$ is
3. $(0,4]$.

From the fact that the angle between $\overrightarrow{A B}$ and $\overrightarrow{B C}$ is $150^{\circ}$, we know $\angle B=30^{\circ}$.
By the Law of Sines, we have
$$
\frac{|\overrightarrow{A B}|}{\sin C}=\frac{|\overrightarrow{A C}|}{\sin 30^{\circ}}=4 \text {. }
$$

Thus, $|\overrightarrow{A B}|=4 \sin C$.
Since $0<\angle C<150^{\circ}$, the range of $|\overrightarrow{A B}|$ is $(0,4]$.