| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Topic | Vectors Introduction & 2D |
| Type | Parallel or perpendicular vectors condition |
| Difficulty | Moderate -0.8 Part (a) is straightforward vector arithmetic requiring only scalar multiplication and addition. Part (b) requires understanding that parallel to y-axis means x-component equals zero, then solving a simple linear equation followed by using magnitude formula. This is a standard introductory vectors question with routine techniques and no problem-solving insight required. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10d Vector operations: addition and scalar multiplication |
| Answer | Marks | Guidance |
|---|---|---|
| \(\begin{pmatrix}15\\-12\end{pmatrix}\) or \(15\mathbf{i} - 12\mathbf{j}\) | B1, B1 | B1 for each element. Allow i, j notation without "squiggles" |
| [1] |
| Answer | Marks | Guidance |
|---|---|---|
| \(6r - s = 0\), \(s = 6r\) | M1 | |
| \(0^2 + (9r)^2 = 9\), \(81r^2 = 9\) | M1, A1 | Attempt \( |
| \(r = \pm\frac{1}{3}\) | A1 | Allow just \(r = \frac{1}{3}\) |
| \(r = \frac{1}{3}\) and \(s=2\) or \(r = -\frac{1}{3}\) and \(s=-2\) | A1 | Correctly paired |
| [5] |
# Question 4:
## Part (a):
| $\begin{pmatrix}15\\-12\end{pmatrix}$ or $15\mathbf{i} - 12\mathbf{j}$ | B1, B1 | B1 for each element. Allow **i**, **j** notation without "squiggles" |
|---|---|---|
| | [1] | |
## Part (b):
| $6r - s = 0$, $s = 6r$ | M1 | |
|---|---|---|
| $0^2 + (9r)^2 = 9$, $81r^2 = 9$ | M1, A1 | Attempt $|\mathbf{a}|^2 = 9$, or $|\mathbf{a}|=3$; allow in terms of both $r$ and $s$ |
| $r = \pm\frac{1}{3}$ | A1 | Allow just $r = \frac{1}{3}$ |
| $r = \frac{1}{3}$ and $s=2$ or $r = -\frac{1}{3}$ and $s=-2$ | A1 | Correctly paired |
| | [5] | |
---4
\begin{enumerate}[label=(\alph*)]
\item Simplify $2 \binom { 6 } { - 3 } - 3 \binom { - 1 } { 2 }$.
\item The vector $\mathbf { a }$ is defined by $\mathbf { a } = r \binom { 6 } { - 3 } + s \binom { - 1 } { 2 }$, where $r$ and $s$ are constants.
Determine two pairs of values of $r$ and $s$ such that $\mathbf { a }$ is parallel to the $y$-axis and $| \mathbf { a } | = 3$.
\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q4 [7]}}