Coordinate geometry — practice question

The figure depicts a solid $ABCDEF$ whose horizontal base $ABC$ is a triangle with a right angle at $A$. $AB$ and $AC$ are $8$ units and $6$ units long respectively, and $M$ is the midpoint of $AB$. Point $D$ is $7$ units directly above $A$. Triangle $DEF$ is in a horizontal plane, with $DE$, $DF$ and $FE$ parallel to $AB$, $AC$ and $CB$ respectively, and $N$ is the midpoint of $FE$. The lengths of $DE$ and $DF$ are $4$ units and $2$ units respectively. Unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $\overrightarrow{AB}$, $\overrightarrow{AC}$ and $\overrightarrow{AD}$ respectively.