2. Two constant forces $\mathbf { F } _ { 1 }$ and $\mathbf { F } _ { 2 }$ are the only forces acting on a particle $P$ of mass 2 kg . The particle is initially at rest at the point $A$ with position vector $( - 2 \mathbf { i } - \mathbf { j } - 4 \mathbf { k } ) \mathrm { m }$. Four seconds later, $P$ is at the point $B$ with position vector $( 6 \mathbf { i } - 5 \mathbf { j } + 8 \mathbf { k } ) \mathrm { m }$.

Given that $\mathbf { F } _ { 1 } = ( 12 \mathbf { i } - 4 \mathbf { j } + 6 \mathbf { k } ) \mathrm { N }$, find
\begin{enumerate}[label=(\alph*)]
\item $\mathbf { F } _ { 2 }$,
\item the work done on $P$ as it moves from $A$ to $B$.
\end{enumerate}

\hfill \mbox{\textit{Edexcel M5 2004 Q2 [8]}}