Let A, B, C be three points whose position vectors respectively are

$\overrightarrow a = \widehat i + 4\widehat j + 3\widehat k$

$$\overrightarrow b = 2\widehat i + \alpha \widehat j + 4\widehat k,\,\alpha \in R$$

$\overrightarrow c = 3\widehat i - 2\widehat j + 5\widehat k$

If $\alpha$ is the smallest positive integer for which $\overrightarrow a ,\,\overrightarrow b ,\,\overrightarrow c$ are noncollinear, then the length of the median, in $\Delta$ABC, through A is :

1. A ${{\sqrt {82} } \over 2}$ Correct answer
2. B ${{\sqrt {62} } \over 2}$
3. C ${{\sqrt {69} } \over 2}$
4. D ${{\sqrt {66} } \over 2}$