(a)[5]
Find a vector equation of the line joining $M$ and $N$.
(b)[4]
Show that the perpendicular distance from $O$ to $MN$ is $\frac{1}{3}\sqrt{82}$.
Mathematics 9709 · AS & A Level · Vectors
Vectors — practice question
The diagram shows $OABCD$ as a pyramid with vertex $D$. Its horizontal base $OABC$ is a square with side $4$ units. Edge $OD$ is vertical, and $OD = 4$ units. The unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OC$ and $OD$ respectively. $M$ is the midpoint of $AB$, and $N$ is a point on $CD$ such that $DN = 3NC$.