| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Year | 2013 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors 3D & Lines |
| Type | Line-plane intersection and related angle/perpendicularity |
| Difficulty | Moderate -0.3 This is a straightforward three-part question on 3D coordinate geometry covering standard techniques: finding a line equation from two points, finding line-plane intersection by substitution, and calculating an angle using dot product. All parts follow routine procedures with no conceptual challenges, making it slightly easier than average, though the multi-step nature and 8 total marks keep it from being trivial. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04f Line-plane intersection: find point |
\begin{enumerate}[label=(\roman*)]
\item Find a vector equation of the line $l$ joining the points $(0, 1, 3)$ and $(-2, 2, 5)$. [2]
\item Find the point of intersection of the line $l$ with the plane $x + 3y + 2z = 4$. [3]
\item Find the acute angle between the line $l$ and the normal to the plane. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C4 2013 Q4 [8]}}