Let $\overrightarrow{O R}$ be the vector that is perpendicular to the vectors $\overrightarrow{O P}=2 \hat{\imath}-3 \hat{\jmath}+\hat{k}$ and $\overrightarrow{O Q}=-2 \hat{\imath}+\hat{\jmath}+\hat{k}$. If the length of the vector $\overrightarrow{O R}$ is $\alpha \sqrt{3}$, then $\alpha$ is $\_\_\_\_\_\_\_$.
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