| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2022 |
| Session | June |
| Marks | 3 |
| Topic | Vectors Introduction & 2D |
| Type | Vector between two points |
| Difficulty | Moderate -0.8 This is a straightforward vector magnitude question requiring only basic vector subtraction and solving a simple quadratic equation. The steps are routine: find AB = (5, p-3), apply |AB|² = 25 + (p-3)² = 50, solve (p-3)² = 25 to get p = 8 or p = -2. No conceptual difficulty or problem-solving insight needed beyond standard technique. |
| Spec | 1.10c Magnitude and direction: of vectors1.10e Position vectors: and displacement |
Relative to a fixed origin $O$,
\begin{itemize}
\item the point $A$ has position vector $-2\mathbf{i} + 3\mathbf{j}$,
\item the point $B$ has position vector $3\mathbf{i} + p\mathbf{j}$, where $p$ is constant,
\end{itemize}
Given that $|\overrightarrow{AB}| = 5\sqrt{2}$, find the possible values for $p$. [3]
\hfill \mbox{\textit{SPS SPS SM Pure 2022 Q5 [3]}}