574 Упростите выражение: а) \(\overrightarrow{OP} – \overrightarrow{EP} + \overrightarrow{KD}-\overrightarrow{KA}\); 6) \(\overrightarrow{AD} + \overrightarrow{MP} + \overrightarrow{EK}- -\overrightarrow{EP}-\overrightarrow{MD}\); в) \(\overrightarrow{AC} – \overrightarrow{BC} – \overrightarrow{PM} – \overrightarrow{AP} + \overrightarrow{BM}\).

Давай упростим каждое выражение пошагово. а) \(\overrightarrow{OP} – \overrightarrow{EP} + \overrightarrow{KD}-\overrightarrow{KA} = \overrightarrow{OP} + \overrightarrow{PE} + \overrightarrow{KD} + \overrightarrow{AK} = \overrightarrow{OE} + \overrightarrow{AD}\) \(\overrightarrow{OE} + \overrightarrow{AD}\) б) \(\overrightarrow{AD} + \overrightarrow{MP} + \overrightarrow{EK} - \overrightarrow{EP} - \overrightarrow{MD} = \overrightarrow{AD} + \overrightarrow{MP} + \overrightarrow{EK} + \overrightarrow{PE} + \overrightarrow{DM} = \overrightarrow{AD} + \overrightarrow{DP} + \overrightarrow{DK} = \overrightarrow{AP} + \overrightarrow{AK}\) \(\overrightarrow{AP} + \overrightarrow{AK}\) в) \(\overrightarrow{AC} – \overrightarrow{BC} – \overrightarrow{PM} – \overrightarrow{AP} + \overrightarrow{BM} = \overrightarrow{AC} + \overrightarrow{CB} + \overrightarrow{MP} + \overrightarrow{PA} + \overrightarrow{BM} = \overrightarrow{AB} + \overrightarrow{MA} + \overrightarrow{BM} = \overrightarrow{MB} + \overrightarrow{BM} = \overrightarrow{MM} = 0\)

Ответ: а) \(\overrightarrow{OE} + \overrightarrow{AD}\); б) \(\overrightarrow{AP} + \overrightarrow{AK}\); в) 0