In Δ ABC, AB = i + j +2 k and AC =3 i - j +4 k. If D is mid-point of BC, then vector AD is equal to:

In $\displaystyle \Delta \mathrm{ABC}, \overrightarrow{\mathrm{AB}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+2 \hat{\mathrm{k}}$ and $\displaystyle \overrightarrow{\mathrm{AC}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+4 \hat{\mathrm{k}}$. If D is mid-point of BC , then vector $\displaystyle \overrightarrow{\mathrm{AD}}$ is equal to :