| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Angle between two vectors |
| Difficulty | Moderate -0.8 This is a straightforward multi-part vectors question testing basic operations: finding a vector between two points, calculating unit vectors, scaling vectors, and finding angles using the scalar product formula. All parts are routine textbook exercises requiring direct application of standard formulas with no problem-solving insight needed. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
The position vectors of the points $A$ and $B$, relative to a fixed origin $O$, are given by
$$\mathbf{a} = -3\mathbf{i} + 4\mathbf{j}, \quad \mathbf{b} = 5\mathbf{i} + 8\mathbf{j},$$
respectively.
\begin{enumerate}[label=(\alph*)]
\item Find the vector $\overrightarrow{AB}$. [2]
\item \begin{enumerate}[label=(\roman*)]
\item Find a unit vector in the direction of $\mathbf{a}$. [2]
\item The point $C$ is such that the vector $\overrightarrow{OC}$ is in the direction of $\mathbf{a}$. Given that the length of $\overrightarrow{OC}$ is 7 units, write down the position vector of $C$. [1]
\end{enumerate}
\item Calculate the angle $AOB$. [3]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2023 Q12 [8]}}