| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Cross Product & Distances |
| Type | Volume of tetrahedron using scalar triple product |
| Difficulty | Standard +0.8 This is a Further Maths FP3 question requiring systematic application of cross product and scalar triple product formulas. While the calculations are multi-step (cross product, scalar triple product, area, volume), they follow standard procedures without requiring novel insight. The difficulty is elevated above average due to being Further Maths content and requiring careful vector arithmetic across four parts, but it remains a textbook-style exercise testing technique rather than problem-solving. |
| Spec | 4.04c Scalar product: calculate and use for angles4.04g Vector product: a x b perpendicular vector |
2.
\begin{figure}[h]
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\includegraphics[alt={},max width=\textwidth]{4255ef1b-2186-4a7e-adf3-a963601c95b2-04_333_360_328_794}
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\caption{Figure 1}
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\end{figure}
The points $A , B$ and $C$ have position vectors $\mathbf { a } , \mathbf { b }$ and $\mathbf { c }$ respectively, relative to a fixed origin $O$, as shown in Figure 1.
It is given that
$$\mathbf { a } = \mathbf { i } + \mathbf { j } , \quad \mathbf { b } = 3 \mathbf { i } - \mathbf { j } + \mathbf { k } \quad \text { and } \quad \mathbf { c } = 2 \mathbf { i } + \mathbf { j } - \mathbf { k } .$$
Calculate
\begin{enumerate}[label=(\alph*)]
\item $\mathbf { b } \times \mathbf { c }$,
\item a.(b $\times \mathbf { c ) }$,
\item the area of triangle $O B C$,
\item the volume of the tetrahedron $O A B C$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 Q2 [7]}}