Giải giúp mình câu b nha

Câu 2: a. Ta có: \[ \overrightarrow{AB} + \overrightarrow{CD} = \overrightarrow{AB} + \overrightarrow{BA} = \overrightarrow{0} \] \[ \overrightarrow{AD} + \overrightarrow{CB} = \overrightarrow{AD} + \overrightarrow{DA} = \overrightarrow{0} \] Vậy: \[ \overrightarrow{AB} + \overrightarrow{CD} = \overrightarrow{AD} + \overrightarrow{CB} \] b. Ta có: \[ \overrightarrow{MC} = -\frac{1}{2}\overrightarrow{MD} \] Từ đó ta có: \[ \overrightarrow{MC} = -\frac{1}{2}(\overrightarrow{MO} + \overrightarrow{OD}) \] \[ \overrightarrow{MC} = -\frac{1}{2}\overrightarrow{MO} - \frac{1}{2}\overrightarrow{OD} \] Mặt khác: \[ \overrightarrow{MC} = \overrightarrow{MO} + \overrightarrow{OC} \] Do đó: \[ \overrightarrow{MO} + \overrightarrow{OC} = -\frac{1}{2}\overrightarrow{MO} - \frac{1}{2}\overrightarrow{OD} \] \[ \overrightarrow{MO} + \overrightarrow{OC} = -\frac{1}{2}\overrightarrow{MO} - \frac{1}{2}\overrightarrow{OD} \] \[ \overrightarrow{MO} + \frac{1}{2}\overrightarrow{MO} = -\overrightarrow{OC} - \frac{1}{2}\overrightarrow{OD} \] \[ \frac{3}{2}\overrightarrow{MO} = -\overrightarrow{OC} - \frac{1}{2}\overrightarrow{OD} \] \[ \overrightarrow{MO} = -\frac{2}{3}\overrightarrow{OC} - \frac{1}{3}\overrightarrow{OD} \] Ta biết rằng: \[ \overrightarrow{OC} = \frac{1}{2}\overrightarrow{AC} = \frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AD}) \] \[ \overrightarrow{OD} = \frac{1}{2}\overrightarrow{BD} = \frac{1}{2}(\overrightarrow{AD} - \overrightarrow{AB}) \] Thay vào ta có: \[ \overrightarrow{MO} = -\frac{2}{3}\left(\frac{1}{2}(\overrightarrow{AB} + \overrightarrow{AD})\right) - \frac{1}{3}\left(\frac{1}{2}(\overrightarrow{AD} - \overrightarrow{AB})\right) \] \[ \overrightarrow{MO} = -\frac{1}{3}(\overrightarrow{AB} + \overrightarrow{AD}) - \frac{1}{6}(\overrightarrow{AD} - \overrightarrow{AB}) \] \[ \overrightarrow{MO} = -\frac{1}{3}\overrightarrow{AB} - \frac{1}{3}\overrightarrow{AD} - \frac{1}{6}\overrightarrow{AD} + \frac{1}{6}\overrightarrow{AB} \] \[ \overrightarrow{MO} = -\frac{1}{3}\overrightarrow{AB} + \frac{1}{6}\overrightarrow{AB} - \frac{1}{3}\overrightarrow{AD} - \frac{1}{6}\overrightarrow{AD} \] \[ \overrightarrow{MO} = -\frac{1}{6}\overrightarrow{AB} - \frac{1}{2}\overrightarrow{AD} \] \[ \overrightarrow{OM} = \frac{1}{6}\overrightarrow{AB} + \frac{1}{2}\overrightarrow{AD} \] Đáp số: a. $\overrightarrow{AB} + \overrightarrow{CD} = \overrightarrow{AD} + \overrightarrow{CB}$ b. $\overrightarrow{OM} = \frac{1}{6}\overrightarrow{AB} + \frac{1}{2}\overrightarrow{AD}$