| Exam Board | WJEC |
|---|---|
| Module | Unit 1 (Unit 1) |
| Year | 2019 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Geometric properties using vectors |
| Difficulty | Moderate -0.8 This is a straightforward vector geometry question requiring basic parallelogram properties and ratio division. Part (a) involves routine vector arithmetic (finding AC = c - a, D as midpoint, E using 2:1 ratio), while part (b) requires comparing vectors for parallelism—all standard AS-level techniques with no problem-solving insight needed. Easier than average due to its mechanical, step-by-step nature. |
| Spec | 1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement |
$OABC$ is a parallelogram with $O$ as origin.
\includegraphics{figure_6}
The position vector of $A$ is $\mathbf{a}$ and the position vector of $C$ is $\mathbf{c}$. The midpoint of $AB$ is $D$.
The point $E$ divides the line $CB$ such that $CE : EB = 2 : 1$.
\begin{enumerate}[label=(\alph*)]
\item Find, in terms of $\mathbf{a}$ and $\mathbf{c}$,
\begin{enumerate}[label=(\roman*)]
\item the vector $\overrightarrow{AC}$,
\item the position vector of $D$,
\item the position vector of $E$. [3]
\end{enumerate}
\item Determine whether or not $\overrightarrow{DE}$ is parallel to $\overrightarrow{AC}$, clearly stating your reason. [2]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 1 2019 Q06 [5]}}