Coordinate geometry — practice question

The diagram depicts the solid figure $OABCDEFG$ with a horizontal rectangular base $OABC$, where $OA = 8$ units and $AB = 6$ units. The rectangle $DEFG$ is in a horizontal plane, with $D$ situated $7$ units vertically above $O$ and $DE$ parallel to $OA$. The sides $DE$ and $DG$ are $4$ units and $2$ units long respectively. Unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OC$ and $OD$ respectively.