(i)[2]
Write the vectors $\overrightarrow{DA}$ and $\overrightarrow{CA}$ in terms of $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(ii)[4]
Determine angle $CAD$ by using a scalar product.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram represents a three-dimensional shape. The base $OAB$ is a horizontal triangle with angle $AOB$ equal to $90^\circ$. The side $OBCD$ is a rectangle, and the side $OAD$ lies in a vertical plane. Unit vectors $\mathbf{i}$ and $\mathbf{j}$ are parallel to $OA$ and $OB$ respectively, and the unit vector $\mathbf{k}$ is vertical. The position vectors of $A$, $B$ and $D$ are given by $\overrightarrow{OA} = 8\mathbf{i}$, $\overrightarrow{OB} = 5\mathbf{j}$ and $\overrightarrow{OD} = 2\mathbf{i} + 4\mathbf{k}$.