| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2011 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Lines & Planes |
| Type | Line intersection with plane |
| Difficulty | Standard +0.3 This is a straightforward application of standard vector methods: substituting the line equation into the plane equation to find λ, then using the dot product formula for angles. Both parts are routine textbook exercises requiring no problem-solving insight, though slightly above average difficulty due to being a two-part question involving coordinate manipulation. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04f Line-plane intersection: find point |
6 (i) Find the point of intersection of the line $\mathbf { r } = \left( \begin{array} { r } - 8 \\ - 2 \\ 6 \end{array} \right) + \lambda \left( \begin{array} { r } - 3 \\ 0 \\ 1 \end{array} \right)$ and the plane $2 x - 3 y + z = 11$.\\
(ii) Find the acute angle between the line and the normal to the plane.
Section B (36 marks)\\
\hfill \mbox{\textit{OCR MEI C4 2011 Q6 [8]}}