| 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 | Line intersection verification |
| Difficulty | Moderate -0.3 This is a straightforward two-part question on 3D vector lines. Part (i) requires simple substitution to verify a given point lies on both lines (routine calculation). Part (ii) uses the standard dot product formula for angle between direction vectors. Both parts are direct applications of standard techniques with no problem-solving 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 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| The length of the keyword is a factor of both 84 and 40 | M1 | |
| The only common factors of 84 and 40 are 1, 2 and 4 (and a keyword of length 1 can be dismissed in this context) | E1 |
### Question 5:
| Answer | Marks | Guidance |
|--------|-------|----------|
| The length of the keyword is a factor of both 84 and 40 | M1 | |
| The only common factors of 84 and 40 are 1, 2 and 4 (and a keyword of length 1 can be dismissed in this context) | E1 | |5 (i) Verify that the lines $\mathbf { r } = \left( \begin{array} { r } - 5 \\ 3 \\ 4 \end{array} \right) + \lambda \left( \begin{array} { r } 3 \\ 0 \\ - 1 \end{array} \right)$ and $\mathbf { r } = \left( \begin{array} { r } - 1 \\ 4 \\ 2 \end{array} \right) + \mu \left( \begin{array} { r } 2 \\ - 1 \\ 0 \end{array} \right)$ meet at the point (1,3,2).\\
(ii) Find the acute angle between the lines.
\hfill \mbox{\textit{OCR MEI C4 2010 Q5 [2]}}