If the shortest distance between the lines $\bar{r}_1=\alpha \hat{i}+2 \hat{j}+2 \hat{k}+\lambda(\hat{i}-2 \hat{j}+2 \hat{k}), \lambda \in \mathbb{R}, \alpha>0 \quad$ and $\bar{r}_2=-4 \hat{i}-\hat{k}+\mu(3 \hat{i}-2 \hat{j}-2 \hat{k}), \mu \in R$, is 9 , then the value of $\alpha$ is