(i)[3]
Express the vectors $\overrightarrow{AM}$ and $\overrightarrow{AC}$ using $\mathbf{i}$, $\mathbf{j}$ and $\mathbf{k}$.
(ii)[4]
Use a scalar product to determine angle $MAC$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The diagram represents pyramid $OABCX$. Its horizontal square base $OABC$ has side $8$ units, and the centre of the base is $D$. The apex, $X$, lies vertically above $D$ and $XD = 10$ units. $M$ is the mid-point of $OX$. The unit vectors $\mathbf{i}$ and $\mathbf{j}$ are parallel to $OA$ and $OC$ respectively, while the unit vector $\mathbf{k}$ points vertically upwards.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The correct vector is $\vec{AM}=-6\mathbf{i}+2\mathbf{j}+5\mathbf{k}$” …
- Full mark scheme, point by point
- Step-by-step worked solution
- Write your answer & get it marked instantly by AI