1. Given unit vectors $\boldsymbol{a}, \boldsymbol{b}$, then the range of $|\boldsymbol{a}-2 \boldsymbol{b}|$ is
$$
|\boldsymbol{a}-2 \boldsymbol{b}|^{2}=5-4 \cos \langle\boldsymbol{a}, \boldsymbol{b}\rangle \in[1,9] \Rightarrow|\boldsymbol{a}-2 \boldsymbol{b}| \in[1,3] \text {. }
$$

Translate the above text into English, keeping the original text's line breaks and format:

$$
|\boldsymbol{a}-2 \boldsymbol{b}|^{2}=5-4 \cos \langle\boldsymbol{a}, \boldsymbol{b}\rangle \in[1,9] \Rightarrow|\boldsymbol{a}-2 \boldsymbol{b}| \in[1,3] \text {. }
$$