If AB = j + k and AC =3 i - j +4 k represent the two vectors along the sides AB and AC of ABC, prove that the median AD =(AB + AC)/2, where D is…

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