4.03: Vector section formula
\(\overrightarrow{OA}=4\mathbf i-2\mathbf j\) 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)[5]
Find \(\overrightarrow{OD}\).
See the official mark scheme below.
(b)[1]
Find \(m\).
See the official mark scheme below.


