Zadanie 9a, Paper 1, maj 2023, TZ2, Matematyka AA IB HL

In parallelogram OABC, $\overrightarrow{OA}=\mathbf a$, $\overrightarrow{OC}=\mathbf c$, and $|\mathbf c|=3|\mathbf a|$ with |a|>0. The angle between a and c is θ, with 0<θ<π. Point M lies on the closed segment AB and $\overrightarrow{AM}=k\overrightarrow{AB}$, where 0≤k≤1. It satisfies $\overrightarrow{OM}\cdot\overrightarrow{MC}=0$. For part (b), put u=1−2k.