If $\overrightarrow{\text{AB}} = \hat{\jmath} + \hat{k}$ and $\overrightarrow{\text{AC}} = 3\hat{\imath} - \hat{\jmath} + 4\hat{k}$ represent the two vectors along the sides $\text{AB}$ and $\text{AC}$ of $\Delta\text{ABC}$, prove that the median $\overrightarrow{\text{AD}} = \frac{\overrightarrow{\text{AB}} + \overrightarrow{\text{AC}}}{2}$, where $\text{D}$ is midpoint of $\text{BC}$. Hence, find the length of median $\text{AD}$.