WJEC Further Unit 3 2024 June — Question 3 5 marks

Exam BoardWJEC
ModuleFurther Unit 3 (Further Unit 3)
Year2024
SessionJune
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicWork done and energy
TypeWork done by constant force - vector setup
DifficultyModerate -0.8 This is a straightforward two-part question requiring basic vector addition to find the resultant force, then applying the standard work formula W = F·s to find an unknown constant. Both parts involve routine calculations with no problem-solving insight needed, making it easier than average for A-level Further Maths mechanics.
Spec1.10d Vector operations: addition and scalar multiplication1.10f Distance between points: using position vectors6.02b Calculate work: constant force, resolved component

3. Three forces \(( 4 \mathbf { i } - 7 \mathbf { j } + 9 \mathbf { k } ) \mathrm { N } , ( 5 \mathbf { i } + 3 \mathbf { j } - 8 \mathbf { k } ) \mathrm { N }\) and \(( - 2 \mathbf { i } + 6 \mathbf { j } - 11 \mathbf { k } ) \mathrm { N }\) act on a particle.
  1. Find the resultant \(\mathbf { R }\) of the three forces.
  2. The points \(A\) and \(B\) have position vectors \(( 3 \mathbf { i } + 4 \mathbf { j } - 12 \mathbf { k } ) \mathrm { m }\) and \(( a \mathbf { i } + 7 \mathbf { j } - 10 \mathbf { k } ) \mathrm { m }\) respectively, where \(a\) is a constant. The work done by \(\mathbf { R }\) in moving the particle from \(A\) to \(B\) is 21 J . Calculate the value of \(a\).
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3. Three forces $( 4 \mathbf { i } - 7 \mathbf { j } + 9 \mathbf { k } ) \mathrm { N } , ( 5 \mathbf { i } + 3 \mathbf { j } - 8 \mathbf { k } ) \mathrm { N }$ and $( - 2 \mathbf { i } + 6 \mathbf { j } - 11 \mathbf { k } ) \mathrm { N }$ act on a particle.
\begin{enumerate}[label=(\alph*)]
\item Find the resultant $\mathbf { R }$ of the three forces.
\item The points $A$ and $B$ have position vectors $( 3 \mathbf { i } + 4 \mathbf { j } - 12 \mathbf { k } ) \mathrm { m }$ and $( a \mathbf { i } + 7 \mathbf { j } - 10 \mathbf { k } ) \mathrm { m }$ respectively, where $a$ is a constant. The work done by $\mathbf { R }$ in moving the particle from $A$ to $B$ is 21 J . Calculate the value of $a$.\\

\section*{PLEASE DO NOT WRITE ON THIS PAGE}
\end{enumerate}

\hfill \mbox{\textit{WJEC Further Unit 3 2024 Q3 [5]}}