If the shortest distance between the lines \( \vec{r}_{1}=\alpha\hat{i}+2\hat{j}+2\hat{k}+\lambda(\hat{i}-2\hat{j}+2\hat{k}),\, \lambda\in\mathbb{R},\, \alpha>0 \) and \( \vec{r}_{2}=-4\hat{i}-\hat{k}+\mu(3\hat{i}-2\hat{j}-2\hat{k}),\, \mu\in\mathbb{R} \) is \( 9 \), then \( \alpha \) is equal to ______.
