| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 6 |
| Topic | Vectors Introduction & 2D |
| Type | Parallel or perpendicular vectors condition |
| Difficulty | Moderate -0.8 This is a straightforward multi-part vector question testing basic concepts: direction angle (tan 45° = 1), parallel vectors (proportional components), and unit vector magnitude. All parts require only direct application of standard formulas with minimal algebraic manipulation, making it easier than average A-level content. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication |
Vector $\mathbf{v} = a\mathbf{i} + 0.6\mathbf{j}$, where $a$ is a constant.
\begin{enumerate}[label=(\roman*)]
\item Given that the direction of $\mathbf{v}$ is $45°$, state the value of $a$. [1]
\item Given instead that $\mathbf{v}$ is parallel to $8\mathbf{i} + 3\mathbf{j}$, find the value of $a$. [2]
\item Given instead that $\mathbf{v}$ is a unit vector, find the possible values of $a$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q3 [6]}}