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МатематикаРешебник по геометрии 11 класс. Атанасян ФГОС 574
574
\[\boxed{\mathbf{574.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]
\[Воспользуемся\ сочетательным\ \]
\[и\ переместительным\ законами.\]
\[\textbf{а)}\ - \overrightarrow{\text{EP}} = \overrightarrow{\text{PE}};\ \ \ - \overrightarrow{\text{KA}} = \overrightarrow{\text{AK}}:\]
\[\overrightarrow{\text{OP}} - \overrightarrow{\text{EP}} + \overrightarrow{\text{KD}} - \overrightarrow{\text{KA}} =\]
\[= \overrightarrow{\text{OP}} + \overrightarrow{\text{PE}} + \overrightarrow{\text{KD}} + \overrightarrow{\text{AK}} =\]
\[= \left( \overrightarrow{\text{OP}} + \overrightarrow{\text{PE}} \right) + \left( \overrightarrow{\text{AK}} + \overrightarrow{\text{KD}} \right) =\]
\[= \overrightarrow{\text{OE}} + \overrightarrow{\text{AD}}.\]
\[\textbf{б)}\ - \overrightarrow{\text{EP}} = \overrightarrow{\text{PE}};\ \ - \overrightarrow{\text{MD}} = \overrightarrow{\text{DM}}:\]
\[\overrightarrow{\text{AD}} + \overrightarrow{\text{MP}} + \overrightarrow{\text{EK}} - \overrightarrow{\text{EP}} - \overrightarrow{\text{MD}} =\]
\[= \overrightarrow{\text{AD}} + \overrightarrow{\text{MP}} + \overrightarrow{\text{EK}} + \overrightarrow{\text{PE}} + \overrightarrow{\text{DM}} =\]
\[= \left( \overrightarrow{\text{AD}} + \overrightarrow{\text{DM}} + \overrightarrow{\text{MP}} + \overrightarrow{\text{PE}} + \overrightarrow{\text{EK}} \right) =\]
\[= \overrightarrow{\text{AK}}.\]
\[\textbf{в)}\ - \overrightarrow{\text{BC}} = \overrightarrow{\text{CB}};\ \ - \overrightarrow{\text{PM}} = \overrightarrow{\text{MP}};\ \ \]
\[- \overrightarrow{\text{AP}} = \overrightarrow{\text{PA}}:\]
\[\overrightarrow{\text{AC}} - \overrightarrow{\text{BC}} - \overrightarrow{\text{PM}} - \overrightarrow{\text{AP}} + \overrightarrow{\text{BM}} =\]
\[= \overrightarrow{\text{AC}} + \overrightarrow{\text{CB}} + \overrightarrow{\text{MP}} + \overrightarrow{\text{PA}} + \overrightarrow{\text{BM}} =\]
\[= \left( \overrightarrow{\text{AC}} + \overrightarrow{\text{CB}} + \overrightarrow{\text{BM}} + \overrightarrow{\text{MP}} + \overrightarrow{\text{PA}} \right) =\]
\[= \overrightarrow{\text{AA}} = \overrightarrow{0}\text{.\ }\]
