| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2010 |
| Session | January |
| Marks | 2 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Perpendicularity conditions |
| Difficulty | Standard +0.3 This is a straightforward multi-part vectors question requiring routine techniques: finding direction vectors by subtraction, verifying perpendicularity via dot product (which should yield zero), and using the normal vector to write a plane equation. All steps are standard C4 procedures with no novel insight required, making it slightly easier than average. |
| Spec | 1.10d Vector operations: addition and scalar multiplication4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Two from: Ciphertext N has high frequency; E would then correspond to ciphertext R which also has high frequency; T would then correspond to ciphertext G which also has high frequency; A is preceded by a string of six letters displaying low frequency | B1, B1 | oe |
### Question 4:
| Answer | Marks | Guidance |
|--------|-------|----------|
| Two from: Ciphertext N has high frequency; E would then correspond to ciphertext R which also has high frequency; T would then correspond to ciphertext G which also has high frequency; A is preceded by a string of six letters displaying low frequency | B1, B1 | oe |4 The points A , B and C have coordinates $( 1,3 , - 2 ) , ( - 1,2 , - 3 )$ and $( 0 , - 8,1 )$ respectively.\\
(i) Find the vectors $\overrightarrow { \mathrm { AB } }$ and $\overrightarrow { \mathrm { AC } }$.\\
(ii) Show that the vector $2 \mathbf { i } - \mathbf { j } - 3 \mathbf { k }$ is perpendicular to the plane ABC . Hence find the equation of the plane ABC .
\hfill \mbox{\textit{OCR MEI C4 2010 Q4 [2]}}