11
\includegraphics[max width=\textwidth, alt={}, center]{ce3c4a9c-bf83-4d28-96e2-ef31c3673dea-16_593_780_264_685} In the diagram, \(O A B C D E F G\) is a cuboid in which \(O A = 3\) units, \(O C = 2\) units and \(O D = 2\) units. Unit vectors \(\mathbf { i } , \mathbf { j }\) and \(\mathbf { k }\) are parallel to \(O A , O D\) and \(O C\) respectively. \(M\) is the midpoint of \(E F\).

1. Find the position vector of \(M\).
   The position vector of \(P\) is \(\mathbf { i } + \mathbf { j } + 2 \mathbf { k }\).
2. Calculate angle PAM.
3. Find the exact length of the perpendicular from \(P\) to the line passing through \(O\) and \(M\).
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.