| Exam Board | Edexcel |
|---|---|
| Module | FP3 (Further Pure Mathematics 3) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Lines & Planes |
| Type | Perpendicular distance point to plane |
| Difficulty | Standard +0.3 This is a straightforward Further Maths vectors question testing standard techniques: identifying the normal vector from a plane equation, writing a line equation parallel to that normal, finding intersection by substitution, and calculating distance. All steps are routine applications of learned methods with no novel insight required, making it slightly easier than average even for FM. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms4.04f Line-plane intersection: find point4.04j Shortest distance: between a point and a plane |
The line $l$ passes through the point $P(2, 1, 3)$ and is perpendicular to the plane $\Pi$ whose vector equation is
$$\mathbf{r} \cdot (\mathbf{i} - 2\mathbf{j} - \mathbf{k}) = 3$$
Find
\begin{enumerate}[label=(\alph*)]
\item a vector equation of the line $l$, [2]
\item the position vector of the point where $l$ meets $\Pi$. [4]
\item Hence find the perpendicular distance of $P$ from $\Pi$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel FP3 2014 Q1 [8]}}