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 ____________.

If $\overrightarrow r = \overrightarrow a + \lambda \overrightarrow b$ and $\overrightarrow r = \overrightarrow c + \lambda \overrightarrow d$ then shortest distance between two lines is <br><br>$$L = {{(\overrightarrow a - \overrightarrow c ).(\overrightarrow b \times \overrightarrow d )} \over {|b \times d|}}$$<br><br>$\therefore$ $$\overrightarrow a - \overrightarrow c = ((\alpha + 4)\widehat i + 2\widehat j + 3\widehat k)$$<br><br>$${{\overrightarrow b \times \overrightarrow d } \over {|b \times d|}} = {{(2\widehat i + 2\widehat j + \widehat k)} \over 3}$$<br><br>$\therefore$ $$((\alpha + 4)\widehat i + 2\widehat j + 3\widehat k).{{(2\widehat i + 2\widehat j + \widehat k)} \over 3} = 9$$<br><br>or $\alpha$ = 6