| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2010 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Cross Product & Distances |
| Type | Show lines are skew (non-intersecting) |
| Difficulty | Standard +0.3 This is a standard FP3 question on 3D lines requiring systematic substitution to check if a common point exists. While it involves multiple steps (parametrizing both lines, equating coordinates, solving simultaneous equations), the method is routine and well-practiced. It's slightly easier than average because it's a direct application of a standard algorithm with no conceptual subtlety or proof required. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04e Line intersections: parallel, skew, or intersecting |
Determine whether the lines
$$\frac{x-1}{-1} = \frac{y+2}{2} = \frac{z+4}{2} \quad \text{and} \quad \frac{x+3}{2} = \frac{y-1}{3} = \frac{z-5}{4}$$
intersect or are skew. [5]
\hfill \mbox{\textit{OCR FP3 2010 Q1 [5]}}