| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 2 (Further Pure Core 2) |
| Year | 2017 |
| Session | Specimen |
| Marks | 8 |
| Topic | Vectors: Lines & Planes |
| Type | Angle between line and plane |
| Difficulty | Standard +0.3 This is a straightforward Further Maths vectors question requiring standard techniques: finding angle between line and plane using dot product formula, and checking if a line is parallel/perpendicular/intersects a plane. Both parts are routine applications of formulas with no conceptual challenges or novel problem-solving required. |
| Spec | 4.04d Angles: between planes and between line and plane4.04e Line intersections: parallel, skew, or intersecting |
6 The equation of a plane $\Pi$ is $x - 2 y - z = 30$.\\
(i) Find the acute angle between the line $\mathbf { r } = \left( \begin{array} { c } 3 \\ 2 \\ - 5 \end{array} \right) + \lambda \left( \begin{array} { r } - 5 \\ 3 \\ 2 \end{array} \right)$ and $\Pi$.\\
(ii) Determine the geometrical relationship between the line $\mathbf { r } = \left( \begin{array} { l } 1 \\ 4 \\ 2 \end{array} \right) + \mu \left( \begin{array} { r } 3 \\ - 1 \\ 5 \end{array} \right)$ and $\Pi$.
\hfill \mbox{\textit{OCR Further Pure Core 2 2017 Q6 [8]}}