| Exam Board | Edexcel |
|---|---|
| Module | P4 (Pure Mathematics 4) |
| Year | 2022 |
| Session | October |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Cross Product & Distances |
| Type | Angle between vectors using scalar product |
| Difficulty | Standard +0.3 This is a straightforward Further Maths vectors question requiring basic vector subtraction and the scalar product formula for angles. Part (a) is simple vector arithmetic (RQ = PQ - PR), and part (b) applies the standard cos θ = (a·b)/(|a||b|) formula. Both are routine applications of standard techniques with no conceptual challenges or novel problem-solving required, making it slightly easier than average even for Further Maths. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10d Vector operations: addition and scalar multiplication4.04c Scalar product: calculate and use for angles |
\includegraphics{figure_1}
Figure 1 shows a sketch of triangle $PQR$.
Given that
• $\overrightarrow{PQ} = 2\mathbf{i} - 3\mathbf{j} + 4\mathbf{k}$
• $\overrightarrow{PR} = 8\mathbf{i} - 5\mathbf{j} + 3\mathbf{k}$
\begin{enumerate}[label=(\alph*)]
\item Find $\overrightarrow{RQ}$ [2]
\item Find the size of angle $PQR$, in degrees, to three significant figures. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel P4 2022 Q3 [5]}}