(i)[2]
Express the vectors $\overrightarrow{OD}$ and $\overrightarrow{CD}$ using $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(ii)[4]
Use a scalar product to determine angle $ODC$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram depicts a pyramid $OABC$ with edge $OC$ running vertically. Its horizontal base $OAB$ is a triangle that is right-angled at $O$, and $D$ is the mid-point of $AB$. The edges $OA$, $OB$ and $OC$ measure $8$ units, $6$ units and $10$ units respectively. The unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OB$ and $OC$ respectively.