CAIE P3 2022 November — Question 6

Exam BoardCAIE
ModuleP3 (Pure Mathematics 3)
Year2022
SessionNovember
TopicVectors: Cross Product & Distances

6 Relative to the origin \(O\), the points \(A , B\) and \(C\) have position vectors given by $$\overrightarrow { O A } = \left( \begin{array} { l } 1
3
1 \end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { l } 3
1
2 \end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { r } 5
3
- 2 \end{array} \right)$$
  1. Using a scalar product, find the cosine of angle \(B A C\).
  2. Hence find the area of triangle \(A B C\). Give your answer in a simplified exact form.