4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{4c08fbab-283e-4c92-89a4-10f68f37e133-07_330_494_210_724}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{figure}
Figure 2 shows the points \(A\) and \(B\) with position vectors \(\mathbf { a }\) and \(\mathbf { b }\) respectively, relative to a fixed origin \(O\).
Given that \(| \mathbf { a } | = 5 , | \mathbf { b } | = 6\) and a.b \(= 20\)
- find the cosine of angle \(A O B\),
- find the exact length of \(A B\).
- Show that the area of triangle \(O A B\) is \(5 \sqrt { 5 }\)