Edexcel C34 2015 June — Question 4

Exam BoardEdexcel
ModuleC34 (Core Mathematics 3 & 4)
Year2015
SessionJune
TopicVectors Introduction & 2D

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 \(= 20\)
  1. find the cosine of angle \(A O B\),
  2. find the exact length of \(A B\).
  3. Show that the area of triangle \(O A B\) is \(5 \sqrt { 5 }\)