If the sides AB and AC of $\Delta$ ABC are represented by vectors $\hat{j} + \hat{k}$ and 3$\hat{i} - \hat{j} + 4\hat{k}$ respectively, then the length of the median through A on BC is : (A) 2$\sqrt{2}$ units (B) $\sqrt{18}$ units (C) $\frac{\sqrt{34}}{2}$ units (D) $\frac{\sqrt{48}}{2}$ units