34．（2023•黄浦区模拟）已知单位向量$\overrightarrow{a}$与$\overrightarrow{b}$，向量$\overrightarrow{b}$在$\overrightarrow{a}$方向上的投影向量为$\overrightarrow{b_0}$，且$\overrightarrow{b_0}=\lambda \overrightarrow{a}(\lambda \in R)$，若$\langle \overrightarrow{a},\overrightarrow{b}\rangle$的取值范围是$[{\frac{\pi }{3},\frac{5\pi }{6}}]$，则$\lambda$的取值范围是 ___$[{-\frac{\sqrt{3}}{2},\frac{1}{2}}]$___．