MathematicsMedium202×since 2002Q5695Let A, B, C be three points whose position vectors respectively are a→=i^+4j^+3k^\overrightarrow a = \widehat i + 4\widehat j + 3\widehat ka=i+4j+3k b→=2i^+αj^+4k^, α∈R\overrightarrow b = 2\widehat i + \alpha \widehat j + 4\widehat k,\,\alpha \in Rb=2i+αj+4k,α∈R c→=3i^−2j^+5k^\overrightarrow c = 3\widehat i - 2\widehat j + 5\widehat kc=3i−2j+5k If α\alphaα is the smallest positive integer for which a→, b→, c→\overrightarrow a ,\,\overrightarrow b ,\,\overrightarrow ca,b,c are noncollinear, then the length of the median, in Δ\DeltaΔABC, through A is :A822{{\sqrt {82} } \over 2}282B622{{\sqrt {62} } \over 2}262C692{{\sqrt {69} } \over 2}269D662{{\sqrt {66} } \over 2}266Check answerSkip