4.03: Vector section formula

0606/12/M/J/26 — Question 11 · 6 marks

\(\overrightarrow{OA}=4\mathbf i-2\mathbf j\) and \(\overrightarrow{OB}=-4\mathbf i+6\mathbf j\). \(C\) lies on \(AB\) with \(AC:CB=3:1\). \(D\) lies on \(OA\), \(\overrightarrow{OD}=m\overrightarrow{OA}\), and \(\overrightarrow{CD}=5\mathbf i-5.5\mathbf j\).
(a)
Find \(\overrightarrow{OD}\).
[5]
(b)
Find \(m\).
[1]