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 :

Question

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 :

${{\sqrt {82} } \over 2}$

${{\sqrt {62} } \over 2}$

${{\sqrt {69} } \over 2}$

${{\sqrt {66} } \over 2}$

Solution

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