If the shortest distance between the lines $\vec{r}_1=\alpha \hat{i}+2 \hat{j}+2 \hat{k}+\lambda(\hat{i}-2 \hat{j}+2 \hat{k}), \lambda \in R, \alpha>0$ and $\vec{r}_2=4 \hat{i}+\hat{k}+\mu(3 \hat{i}-2 \hat{j}-2 \hat{k}), \mu \in R$ is 9 , then $\alpha$ is equal to $\_\_\_\_$ .
