(i)[2]
Show that, in this case, $a = 4$.
(ii)[2]
Write the vector $\overrightarrow{BG}$ in component form using $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(iii)[4]
Use a scalar product to determine angle $GBA$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram represents a pyramid $OABCP$. Its square horizontal base $OABC$ has side $10\ \text{cm}$, and the vertex $P$ is positioned $10\ \text{cm}$ vertically above $O$. The points $D$, $E$, $F$, $G$ are on $OP$, $AP$, $BP$, $CP$ respectively, and $DEFG$ is a horizontal square with side $6\ \text{cm}$. The perpendicular distance of $DEFG$ above the base is $a\ \text{cm}$. The unit vectors $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$ are parallel to $OA$, $OC$ and $OD$ respectively.