Vector Algebra: JEE Main 2021 Mathematics question

If the shortest distance between the lines $\overrightarrow {{r_1}} = \alpha \widehat i + 2\widehat j + 2\widehat k + \lambda (\widehat i - 2\widehat j + 2\widehat k)$, $\lambda$ $\in$ R, $\alpha$ > 0 and $\overrightarrow {{r_2}} = - 4\widehat i - \widehat k + \mu (3\widehat i - 2\widehat j - 2\widehat k)$, $\mu$ $\in$ R is 9, then $\alpha$ is equal to ____________.