| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Year | 2023 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Lines & Planes |
| Type | Line intersection with plane |
| Difficulty | Standard +0.3 This is a straightforward Further Maths vectors question requiring standard techniques: (a) forming a line equation from two points (routine substitution), and (b) substituting the parametric line into the plane equation to find intersection. Both parts are direct applications of learned methods with no conceptual challenges or novel problem-solving required. |
| Spec | 1.10a Vectors in 2D: i,j notation and column vectors4.04a Line equations: 2D and 3D, cartesian and vector forms4.04f Line-plane intersection: find point |
5. The points $A$ and $B$ have coordinates $( 3,4 , - 2 )$ and $( - 2,0,7 )$ respectively. The equation of the plane $\Pi$ is given by $2 x + 3 y + 3 z = 27$.
\begin{enumerate}[label=(\alph*)]
\item Show that the vector equation of the line $A B$ may be expressed in the form
$$\mathbf { r } = ( 3 - 5 \lambda ) \mathbf { i } + ( 4 - 4 \lambda ) \mathbf { j } + ( - 2 + 9 \lambda ) \mathbf { k }$$
\item Find the coordinates of the point of intersection of the line $A B$ and the plane $\Pi$.
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 1 2023 Q5 [6]}}