OCR C4 2016 June — Question 8

Exam BoardOCR
ModuleC4 (Core Mathematics 4)
Year2016
SessionJune
TopicVectors: Lines & Planes

8 The points \(A\) and \(B\) have position vectors relative to the origin \(O\) given by $$\overrightarrow { O A } = \left( \begin{array} { c } 3 \sin \alpha
2 \cos \alpha
- 1 \end{array} \right) \text { and } \overrightarrow { O B } = \left( \begin{array} { c } 2 \cos \alpha
4 \sin \alpha
3 \end{array} \right)$$ where \(0 ^ { \circ } < \alpha < 90 ^ { \circ }\). It is given that \(\overrightarrow { O A }\) and \(\overrightarrow { O B }\) are perpendicular.
  1. Calculate the two possible values of \(\alpha\).
  2. Calculate the area of triangle \(O A B\) for the smaller value of \(\alpha\) from part (i).