| Exam Board | SPS |
|---|---|
| Module | SPS FM Pure (SPS FM Pure) |
| Year | 2021 |
| Session | May |
| Marks | 5 |
| Topic | Vectors: Cross Product & Distances |
| Type | Equation of plane through three points |
| Difficulty | Moderate -0.3 This is a straightforward Further Maths vector question requiring standard techniques: computing two vectors from coordinates, finding their cross product using the determinant method, then using the normal vector to write the plane equation. While it involves multiple steps (5 marks total), each step follows a routine algorithm with no problem-solving insight required. It's slightly easier than average A-level difficulty because it's purely procedural. |
| Spec | 4.04b Plane equations: cartesian and vector forms4.04g Vector product: a x b perpendicular vector |
Points $A$, $B$ and $C$ have coordinates $(0, 1, -4)$, $(1, 1, -2)$ and $(3, 2, 5)$ respectively.
\begin{enumerate}[label=(\alph*)]
\item Find the vector product $\overrightarrow{AB} \times \overrightarrow{AC}$. [3]
\item Hence find the equation of the plane $ABC$ in the form $ax + by + cz = d$. [2]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Pure 2021 Q1 [5]}}