The vectors  \(\vec{BA}\ =\ 4\hat{i}\ -\ 3\hat{j}\)  and \(\vec{BC}\ =\ 2\hat{i}\ -\ 5\hat{j}\ +\ 4\hat{k}\)  are the sides of a triangle ABC. The length of the median through B is

1
\(\sqrt{116}\)
2
\(\sqrt{29}\)
3
\(\sqrt{117}\)
4
\(\sqrt{33}\)

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