A Level Further Maths, Core Pure 1, Chapter 9 · exam-style questions with mark schemes and worked solutions · shadows of past-paper questions and new questions in the style of Edexcel, Edexcel iAL, AQA, OCR A and MEI · the vector equation $\mathbf{r} = \mathbf{a} + \lambda\mathbf{b}$ and the Cartesian equations of a line in three dimensions, the equation of a plane in the forms $\mathbf{r} = \mathbf{a} + \lambda\mathbf{b} + \mu\mathbf{c}$, $\mathbf{r} \cdot \mathbf{n} = p$ and $ax + by + cz = d$, the scalar product $\mathbf{a} \cdot \mathbf{b} = |\mathbf{a}||\mathbf{b}|\cos\theta$, the angle between two lines, between a line and a plane and between two planes, where lines and planes meet (intersecting, parallel and skew lines), the foot of a perpendicular, reflections in a plane, and the shortest distance from a point to a line or a plane and between two lines