| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Vector between two points |
| Difficulty | Moderate -0.8 This is a straightforward vectors question testing basic operations: finding a displacement vector (subtraction), calculating magnitude (Pythagoras), and applying parallel vector conditions with scalar multiplication. All parts follow standard procedures with no problem-solving insight required, making it easier than average but not trivial due to the multi-step part (c). |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement1.10f Distance between points: using position vectors |
The position vectors of the points A and B, relative to a fixed origin O, are given by
$$\mathbf{a} = 4\mathbf{i} + 7\mathbf{j}, \quad\quad \mathbf{b} = \mathbf{i} + 3\mathbf{j},$$
respectively.
\begin{enumerate}[label=(\alph*)]
\item Find the vector $\overrightarrow{AB}$. [2]
\item Determine the distance between the points A and B. [2]
\item The position vector of the point C is given by $\mathbf{c} = -2\mathbf{i} + 5\mathbf{j}$. The point D is such that the distance between C and D is equal to the distance between A and B, and $\overrightarrow{CD}$ is parallel to $\overrightarrow{AB}$. Find the possible position vectors of the point D. [4]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2024 Q13 [8]}}