WJEC Unit 1 2024 June — Question 13 8 marks

Exam BoardWJEC
ModuleUnit 1 (Unit 1)
Year2024
SessionJune
Marks8
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVectors Introduction & 2D
TypeVector between two points
DifficultyModerate -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).
Spec1.10d 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.
  1. Find the vector \(\overrightarrow{AB}\). [2]
  2. Determine the distance between the points A and B. [2]
  3. 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]

Question 13:
AnswerMarks
138
Question 13:
13 | 8
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]}}