| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2011 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Area of triangle from given side vectors or coordinates |
| Difficulty | Moderate -0.3 This is a straightforward application of standard vector techniques: computing dot product to verify perpendicularity (which simplifies part ii), then using the right-angle to find area via ½|AB||BC|. The calculations are routine with no conceptual challenges, making it slightly easier than average, though the multi-step nature and 3D coordinates prevent it from being trivial. |
| Spec | 1.10c Magnitude and direction: of vectors1.10d Vector operations: addition and scalar multiplication4.04g Vector product: a x b perpendicular vector |
| Answer | Marks | Guidance |
|---|---|---|
| 4 | 3 | 2 |
I'd be happy to help clean up mark scheme content, but it appears that only the question number and a simple grid structure were provided in your message:
```
Question 4:
4 | 3 | 2 | 1
```
Please provide the actual mark scheme content that needs cleaning up. Once you share the full mark scheme text with:
- Unicode symbols (θ, Σ, ≥, etc.)
- Marking annotations (M1, A1, B1, DM1, etc.)
- Guidance notes
- Any other content
I'll convert it to the format you've requested with LaTeX notation and clear formatting.4 The points A , B and C have coordinates $( 2,0 , - 1 ) , ( 4,3 , - 6 )$ and $( 9,3 , - 4 )$ respectively.\\
(i) Show that AB is perpendicular to BC .\\
(ii) Find the area of triangle ABC .
\hfill \mbox{\textit{OCR MEI C4 2011 Q4 [7]}}