| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Session | Specimen |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Lines & Planes |
| Type | Line intersection with plane |
| Difficulty | Standard +0.3 This is a standard Further Maths vectors question testing routine techniques: finding a direction vector, writing a vector equation, finding line-plane intersection by substitution, and calculating the angle using the formula with direction vector and normal vector. All steps are algorithmic with no novel insight required, though it involves multiple parts and careful calculation. Slightly above average difficulty due to being Further Maths content and multi-step nature, but still a textbook exercise. |
| Spec | 4.04a Line equations: 2D and 3D, cartesian and vector forms4.04b Plane equations: cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04d Angles: between planes and between line and plane4.04e Line intersections: parallel, skew, or intersecting |
The line $L$ passes through the points A$(1, 2, 3)$ and B$(2, 3, 1)$.
\begin{enumerate}[label=(\alph*)]
\item \begin{enumerate}[label=(\roman*)]
\item Find the vector $\overrightarrow{AB}$.
\item Write down the vector equation of the line $L$. [3]
\end{enumerate}
\item The plane $\Pi$ has equation $x + 3y - 2z = 5$.
\begin{enumerate}[label=(\roman*)]
\item Find the coordinates of the point of intersection of $L$ and $\Pi$.
\item Find the acute angle between $L$ and $\Pi$. [9]
\end{enumerate}
\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 1 Q8 [12]}}