| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2023 |
| Session | September |
| Marks | 7 |
| Topic | Vectors Introduction & 2D |
| Type | Geometric properties using vectors |
| Difficulty | Moderate -0.8 This is a straightforward vectors question testing basic skills: (a) magnitude calculation using Pythagoras, (b) angle using dot product or simple trigonometry, (c) collinearity by showing vectors are scalar multiples. All are standard textbook exercises requiring routine application of formulas with no problem-solving insight needed. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors1.10g Problem solving with vectors: in geometry |
Relative to the origin $O$, the points $A$, $B$ and $C$ have position vectors $4\mathbf{i} + 2\mathbf{j}$, $3\mathbf{i} + 4\mathbf{j}$ and $-\mathbf{i} + 12\mathbf{j}$, respectively.
\begin{enumerate}[label=(\alph*)]
\item Find the magnitude of the vector $\overrightarrow{OC}$ [2]
\item Find the angle that the vector $\overrightarrow{OB}$ makes with the vector $\mathbf{j}$ to the nearest degree [2]
\item Show that the points $A$, $B$ and $C$ are collinear [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2023 Q5 [7]}}