| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Topic | Vectors: Cross Product & Distances |
| Type | Volume of tetrahedron using scalar triple product |
| Difficulty | Standard +0.3 This is a standard Further Maths FP3 vectors question testing routine cross product calculation, finding plane equation from normal vector, and volume formula using scalar triple product. All parts follow textbook methods with straightforward arithmetic, requiring no novel insight—slightly easier than average A-level difficulty when considering it's from Further Maths where students are expected to handle these techniques fluently. |
| Spec | 4.04b Plane equations: cartesian and vector forms4.04g Vector product: a x b perpendicular vector |
The points $A$, $B$ and $C$ lie on the plane $\Pi$ and, relative to a fixed origin $O$, they have position vectors
$$\mathbf{a} = 3\mathbf{i} - \mathbf{j} + 4\mathbf{k}, \quad \mathbf{b} = -\mathbf{i} + 2\mathbf{j}, \quad \mathbf{c} = 5\mathbf{i} - 3\mathbf{j} + 7\mathbf{k}$$
respectively.
\begin{enumerate}[label=(\alph*)]
\item Find $\overrightarrow{AB} \times \overrightarrow{AC}$. [4]
\item Find an equation of $\Pi$ in the form $\mathbf{r} \cdot \mathbf{n} = p$. [2]
\end{enumerate}
The point $D$ has position vector $5\mathbf{i} + 2\mathbf{j} + 3\mathbf{k}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Calculate the volume of the tetrahedron $ABCD$. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q26 [10]}}