| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2024 |
| Session | June |
| Marks | 5 |
| Topic | Vectors 3D & Lines |
| Type | Triangle and parallelogram problems |
| Difficulty | Moderate -0.8 This is a straightforward Further Maths vectors question with standard techniques: part (a) uses the parallelogram property that opposite sides are equal vectors (routine manipulation), and part (b) requires finding a unit vector and scaling it to a given magnitude. Both parts are direct applications of basic vector operations with no problem-solving insight required, making it easier than average even for Further Maths. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors1.10b Vectors in 3D: i,j,k notation1.10d Vector operations: addition and scalar multiplication1.10e Position vectors: and displacement1.10f Distance between points: using position vectors |
\begin{enumerate}
\item Relative to a fixed origin $O$,\\
the point $A$ has position vector $\mathbf { i } + 7 \mathbf { j } - 2 \mathbf { k }$,\\
the point $B$ has position vector $4 \mathbf { i } + 3 \mathbf { j } + 3 \mathbf { k }$,\\
and the point $C$ has position vector $2 \mathbf { i } + 10 \mathbf { j } + 9 \mathbf { k }$.\\
Given that $A B C D$ is a parallelogram,\\
(a) find the position vector of point $D$.
\end{enumerate}
The vector $\overrightarrow { A X }$ has the same direction as $\overrightarrow { A B }$.\\
Given that $| \overrightarrow { A X } | = 10 \sqrt { 2 }$,\\
(b) find the position vector of $X$.\\[0pt]
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\hfill \mbox{\textit{SPS SPS FM Pure 2024 Q2 [5]}}