| Exam Board | Edexcel |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Area of triangle from given side vectors or coordinates |
| Difficulty | Standard +0.3 This is a standard C4 vectors question testing routine techniques: finding angles using dot product, area using cross product or sine formula, perpendicularity check, and ratio calculation. All parts follow textbook methods with no novel insight required, making it slightly easier than average for A-level. |
| Spec | 1.10d Vector operations: addition and scalar multiplication4.04c Scalar product: calculate and use for angles4.04g Vector product: a x b perpendicular vector |
Relative to a fixed origin $O$, the point $A$ has position vector $3\mathbf{i} + 2\mathbf{j} - \mathbf{k}$, the point $B$ has position vector $5\mathbf{i} + \mathbf{j} + \mathbf{k}$, and the point $C$ has position vector $7\mathbf{i} - \mathbf{j}$.
\begin{enumerate}[label=(\alph*)]
\item Find the cosine of angle $ABC$.
[4]
\item Find the exact value of the area of triangle $ABC$.
[3]
\end{enumerate}
The point $D$ has position vector $7\mathbf{i} + 3\mathbf{k}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Show that $AC$ is perpendicular to $CD$.
[2]
\item Find the ratio $AD:DB$.
[2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C4 Q5 [11]}}