CAIE P1 2014 June — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2014
SessionJune
TopicVectors: Lines & Planes

7 The position vectors of points \(A , B\) and \(C\) relative to an origin \(O\) are given by $$\overrightarrow { O A } = \left( \begin{array} { l } 2
1
3 \end{array} \right) , \quad \overrightarrow { O B } = \left( \begin{array} { r } 6
- 1
7 \end{array} \right) \quad \text { and } \quad \overrightarrow { O C } = \left( \begin{array} { l } 2
4
7 \end{array} \right)$$
  1. Show that angle \(B A C = \cos ^ { - 1 } \left( \frac { 1 } { 3 } \right)\).
  2. Use the result in part (i) to find the exact value of the area of triangle \(A B C\).