| Exam Board | OCR MEI |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Lines & Planes |
| Type | 3D geometry applications |
| Difficulty | Standard +0.3 This is a structured multi-part 3D geometry question with standard techniques: finding distances, line equations, verifying plane equations, and finding angles between planes. While it requires multiple steps and careful coordinate work, each part uses routine A-level methods (dot products, normal vectors, standard formulas) without requiring novel insight or particularly challenging problem-solving. Slightly easier than average due to its guided structure. |
| Spec | 1.10c Magnitude and direction: of vectors4.04b Plane equations: cartesian and vector forms4.04d Angles: between planes and between line and plane |
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\caption{Fig. 7}
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Fig. 7 illustrates a house. All units are in metres. The coordinates of A, B, C and E are as shown. BD is horizontal and parallel to AE .\\
(i) Find the length AE .\\
(ii) Find a vector equation of the line BD . Given that the length of BD is 15 metres, find the coordinates of D.\\
(iii) Verify that the equation of the plane ABC is
$$- 3 x + 4 y + 5 z = 30 .$$
Write down a vector normal to this plane.\\
(iv) Show that the vector $\left( \begin{array} { l } 4 \\ 3 \\ 5 \end{array} \right)$ is normal to the plane ABDE . Hence find the equation of the plane ABDE .\\
(v) Find the angle between the planes ABC and ABDE .
\hfill \mbox{\textit{OCR MEI C4 Q12}}