| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2008 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Line intersection verification |
| Difficulty | Standard +0.3 This is a standard two-part vector lines question requiring equating components to find intersection (routine algebraic manipulation) and then using the scalar product formula for angle between direction vectors. Both techniques are core C4 syllabus with no novel insight required, making it slightly easier than average. |
| 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 |
6 Two lines have equations
$$\mathbf { r } = \left( \begin{array} { r }
1 \\
0 \\
- 5
\end{array} \right) + t \left( \begin{array} { l }
2 \\
3 \\
4
\end{array} \right) \quad \text { and } \quad \mathbf { r } = \left( \begin{array} { r }
12 \\
0 \\
5
\end{array} \right) + s \left( \begin{array} { r }
1 \\
- 4 \\
- 2
\end{array} \right) .$$
(i) Show that the lines intersect.\\
(ii) Find the angle between the lines.\\
\hfill \mbox{\textit{OCR C4 2008 Q6 [8]}}