OCR PURE — Question 7

Exam BoardOCR
ModulePURE
TopicVectors Introduction & 2D

7
\includegraphics[max width=\textwidth, alt={}, center]{a1f4ccbd-f5ed-437a-ae76-c4925ce86e25-06_648_586_255_244} The diagram shows the parallelogram \(O A C B\) where \(\overrightarrow { O A } = 2 \mathbf { i } + 4 \mathbf { j }\) and \(\overrightarrow { O B } = 4 \mathbf { i } - 3 \mathbf { j }\).
  1. Show that \(\cos A O B = - \frac { 2 \sqrt { 5 } } { 25 }\).
  2. Hence find the exact value of \(\sin A O B\).
  3. Determine the area of \(O A C B\).