| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Line-plane intersection and related angle/perpendicularity |
| Difficulty | Standard +0.3 This is a straightforward two-part question requiring standard techniques: substituting the line equation into the plane equation to find intersection (routine algebra), then using the scalar product formula to find the angle between direction vectors. Both parts are direct applications of learned methods with no problem-solving insight required, making it slightly easier than average. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms4.04f Line-plane intersection: find point |
1 (i) Find the point of intersection of the line $\left. \left. \mathbf { r } = \begin{array} { r } - 8 \\ - 2 \\ 6 \end{array} \right) + \lambda \begin{array} { r } - 3 \\ 0 \\ 1 \end{array} \right)$ and the plane $2 x - 3 y + z = 11$.\\
(ii) Find the acute angle between the line and the normal to the plane.
\hfill \mbox{\textit{OCR MEI C4 Q1 [8]}}