| Exam Board | SPS |
|---|---|
| Module | SPS ASFM Pure (SPS ASFM Pure) |
| Year | 2020 |
| Session | October |
| Marks | 6 |
| Topic | Vectors 3D & Lines |
| Type | Line intersection: unknown constant then intersect |
| Difficulty | Standard +0.3 This is a standard Further Maths vectors question requiring routine techniques: finding the angle between lines using the dot product formula, then solving simultaneous equations by equating components to find the parameter values and intersection point. While it involves multiple steps and careful algebra, it follows a well-practiced procedure without requiring novel insight or particularly challenging problem-solving. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04e Line intersections: parallel, skew, or intersecting |
4 \\
2 \\
- 6
\end{array} \right) + t \left( \begin{array} { r }
- 8 \\
1 \\
- 2
\end{array} \right) \quad \text { and } \quad \mathbf { r } = \left( \begin{array} { r }
- 2 \\
a \\
- 2
\end{array} \right) + s \left( \begin{array} { r }
- 9 \\
2 \\
- 5
\end{array} \right) ,$$
where a is $a$ constant.\\
\begin{enumerate}[label=(\roman*)]
\item Calculate the acute angle between the lines.
\item Given that these two lines intersect, find $a$ and the point of intersection.
End of examination
\end{enumerate}
\hfill \mbox{\textit{SPS SPS ASFM Pure 2020 Q4 [6]}}