| Exam Board | OCR |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2009 |
| Session | January |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Cross Product & Distances |
| Type | Shortest distance between two skew lines |
| Difficulty | Challenging +1.2 This is a standard Further Maths question on skew lines requiring the cross product of direction vectors and the scalar triple product formula. While it involves multiple steps and vector manipulation beyond A-level Core, it's a textbook application of well-defined techniques with no novel insight required, making it moderately above average difficulty. |
| Spec | 4.04e Line intersections: parallel, skew, or intersecting4.04i Shortest distance: between a point and a line |
3 Two skew lines have equations
$$\frac { x } { 2 } = \frac { y + 3 } { 1 } = \frac { z - 6 } { 3 } \quad \text { and } \quad \frac { x - 5 } { 3 } = \frac { y + 1 } { 1 } = \frac { z - 7 } { 5 } .$$
(i) Find the direction of the common perpendicular to the lines.\\
(ii) Find the shortest distance between the lines.
\hfill \mbox{\textit{OCR FP3 2009 Q3 [6]}}