Coordinate geometry — practice question

The sketch represents a three-dimensional solid whose base $OABC$ and top face $DEFG$ are matching horizontal squares. The parallelograms $OAED$ and $CBFG$ each lie in vertical planes. Point $M$ is the midpoint of $AF$. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are parallel to $OA$ and $OC$ respectively, while $\mathbf{k}$ points vertically upwards. The position vectors of $A$ and $D$ are given by $\overrightarrow{OA} = 8\mathbf{i}$ and $\overrightarrow{OD} = 3\mathbf{i} + 10\mathbf{k}$.