| Exam Board | OCR |
|---|---|
| Module | Further Pure Core 1 (Further Pure Core 1) |
| Year | 2018 |
| Session | March |
| Marks | 7 |
| Topic | Vectors: Lines & Planes |
| Type | Plane containing line and point/vector |
| Difficulty | Standard +0.8 This is a multi-part Further Maths question requiring students to verify line intersection (by solving a system of parametric equations) and then find a plane equation using cross product of direction vectors. While systematic, it demands careful algebraic manipulation, understanding of 3D geometry, and multiple techniques beyond standard A-level content. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms4.04e Line intersections: parallel, skew, or intersecting4.04f Line-plane intersection: find point |
4 The lines $l _ { 1 }$ and $l _ { 2 }$ have equations $\frac { x - 7 } { 2 } = \frac { y - 1 } { - 1 } = \frac { z - 6 } { 3 }$ and $\frac { x - 2 } { 1 } = \frac { y - 6 } { 2 } = \frac { z + 2 } { 1 }$ respectively.\\
(i) Show that $l _ { 1 }$ and $l _ { 2 }$ intersect.\\
(ii) Find the cartesian equation of the plane that contains $l _ { 1 }$ and $l _ { 2 }$.
\hfill \mbox{\textit{OCR Further Pure Core 1 2018 Q4 [7]}}