| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2024 |
| Session | February |
| Marks | 5 |
| Topic | Vectors 3D & Lines |
| Type | Equal length conditions |
| Difficulty | Moderate -0.3 This is a straightforward vectors question with standard techniques: part (a) requires simple vector addition using the given condition, and part (b) involves finding a magnitude and solving a quadratic equation. Both parts are routine applications of basic vector operations with no conceptual challenges or novel problem-solving required. |
| Spec | 1.10b Vectors in 3D: i,j,k notation1.10c Magnitude and direction: of vectors1.10f Distance between points: using position vectors |
4.
Relative to a fixed origin $O$,\\
the point $A$ has position vector $( 2 \mathbf { i } + 3 \mathbf { j } - 4 \mathbf { k } )$,\\
the point $B$ has position vector $( 4 \mathbf { i } - 2 \mathbf { j } + 3 \mathbf { k } )$,\\
and the point $C$ has position vector $( a \mathbf { i } + 5 \mathbf { j } - 2 \mathbf { k } )$, where $a$ is a constant and $a < 0$\\
$D$ is the point such that $\overrightarrow { A B } = \overrightarrow { B D }$.
\begin{enumerate}[label=(\alph*)]
\item Find the position vector of $D$.\\
(2)
Given $| \overrightarrow { A C } | = 4$
\item find the value of $a$.\\
(3)
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2024 Q4 [5]}}