| Exam Board | WJEC |
|---|---|
| Module | Further Unit 1 (Further Unit 1) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Vectors: Cross Product & Distances |
| Type | Acute angle between two planes |
| Difficulty | Standard +0.3 This is a straightforward Further Maths vectors question testing standard techniques: finding angles between planes using dot product of normals (part a), perpendicular distance formula (part b), and verification plus simple plane equation (part c). All parts follow textbook methods with no novel problem-solving required, making it slightly easier than average even for Further Maths. |
| Spec | 4.04b Plane equations: cartesian and vector forms4.04c Scalar product: calculate and use for angles4.04j Shortest distance: between a point and a plane |
| Answer | Marks |
|---|---|
| 9 | 8 |
| Total | 70 |
| Answer | Marks |
|---|---|
| number | Additional page, if required. |
| Answer | Marks |
|---|---|
| number | Additional page, if required. |
Question 9:
9 | 8
Total | 70
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.
Question
number | Additional page, if required.
Write the question number(s) in the left-hand margin.9. Two planes, $\Pi _ { 1 }$ and $\Pi _ { 2 }$, are defined by
$$\begin{aligned}
& \Pi _ { 1 } : 4 x - 3 y + 2 z = 5 \\
& \Pi _ { 2 } : 6 x + y + z = 9
\end{aligned}$$
\begin{enumerate}[label=(\alph*)]
\item Find the acute angle between the planes $\Pi _ { 1 }$ and $\Pi _ { 2 }$. Give your answer correct to three significant figures.
\item Find the perpendicular distance from the point $A ( 5 , - 2 , - 6 )$ to the plane $\Pi _ { 1 }$.
\item \begin{enumerate}[label=(\roman*)]
\item Show that the point $B ( 5,5,0 )$ lies on $\Pi _ { 1 }$ and that the point $C ( 1,3,0 )$ lies on $\Pi _ { 2 }$.
\item State an equation of a plane that contains the points $B$ and $C$.\\
Additional page, if required.
Write the question number(s) in the left-hand margin.
Additional page, if required.
Write the question number(s) in the left-hand margin.
\section*{PLEASE DO NOT WRITE ON THIS PAGE}
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{WJEC Further Unit 1 2024 Q9 [8]}}