Vector Algebra

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 ____________.