Q11 (e) (i)

In the diagram below, $OABCD$ is a solid figure where $|\overrightarrow{OA}|=|\overrightarrow{OB}|=4$ units and $|\overrightarrow{OD}|=3$ units. The edge $\overrightarrow{OD}$ is vertical, $\overrightarrow{DC}$ is parallel to $\overrightarrow{OB}$ and $|\overrightarrow{DC}|=1$ unit. The base, $OAB$, is horizontal and $\angle AOB=90^\circ$. Unit vectors $\vec i$, $\vec j$ and $\vec k$ are parallel to $\overrightarrow{OA}$, $\overrightarrow{OB}$ and $\overrightarrow{OD}$ respectively. The midpoint of $\overline{AB}$ is $M$ and the point $N$ on $\overline{BC}$ is such that $\overrightarrow{NC}=2\overrightarrow{BN}$.

Express vectors $\overrightarrow{MD}$ and $\overrightarrow{ON}$ in terms of $\vec i$, $\vec j$ and $\vec k$.