5.

\begin{figure}[h]
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  \includegraphics[alt={},max width=\textwidth]{a8e9db6b-dfad-4278-82d8-a8fa5ba61008-14_300_1043_251_513}
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\caption{Figure 2}
\end{center}
\end{figure}

Figure 2 shows a sketch of a hexagon $O A B C D E$ where\\
-the interior angle at $O$ and at $C$ are each $60 ^ { \circ }$\\
-the interior angle at each of the other vertices is $150 ^ { \circ }$\\
-$O A = O E = B C = C D$\\
-$A B = E D = 3 \times O A$\\
Given that $\overrightarrow { O A } = \mathbf { a }$ and $\overrightarrow { O E } = \mathbf { e }$\\
determine as simplified expressions in terms of $\mathbf { a }$ and $\mathbf { e }$
\begin{enumerate}[label=(\alph*)]
\item $\overrightarrow { A B }$
\item $\overrightarrow { O D }$

The point $R$ divides $A B$ internally in the ratio $1 : 2$
\item Determine $\overrightarrow { R C }$ as a simplified expression in terms of $\mathbf { a }$ and $\mathbf { e }$

The line through the points $R$ and $C$ meets the line through the points $O$ and $D$ at the point $X$ .
\item Determine $\overrightarrow { O X }$ in the form $\lambda \mathbf { a } + \mu \mathbf { e }$ ,where $\lambda$ and $\mu$ are real values in simplest form.

\begin{center}

\end{center}
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2024 Q5 [15]}}