If $\mathrm{AB}=-3\mathrm{i}+4\mathrm{k}\text{ and }\mathrm{BC}=-\overline{\mathrm{i}}-2\overline{\mathrm{k}}$ are the sides of the triangle ABC, then the length of the median AM is

$$\begin{gathered} \mathrm{AB}=-3\mathrm{i}+4\mathrm{k}\text{ and }\mathrm{BC}=-\overline{\mathrm{i}}-2\overline{\mathrm{k}} \\ \Rightarrow \overline{\mathrm{AC}}=-4\overline{\mathrm{i}}+2\overline{\mathrm{k}} \end{gathered}$$

 Take ‘A’ as origin ‘D’ is midpoint BC

 $\overline{\mathrm{AD}}=\frac{\overline{AB}+\overline{AC}}{2}=\frac{-7\overline{\mathrm{i}}+6\overline{\mathrm{k}}}{2};\therefore \left|\overline{\mathrm{AD}}\right|=\frac{\sqrt{85}}{2}$