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МатематикаРешебник по геометрии 11 класс. Атанасян ФГОС 616
616
\[\boxed{\mathbf{616.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]
\[Дано:\]
\[Решение.\]
\[Воспользуемся\ сочетательным\ \]
\[и\ переместительным\ законами.\]
\[\textbf{а)}\ \overrightarrow{\text{AB}} + \overrightarrow{\text{BD}} + \overrightarrow{\text{DC}} =\]
\[= \left( \overrightarrow{\text{AB}} + \overrightarrow{\text{BD}} \right) + \overrightarrow{\text{DC}} = \overrightarrow{\text{AD}} + \overrightarrow{\text{DC}} =\]
\[= \overrightarrow{\text{AC}}.\]
\[\textbf{б)}\ \overrightarrow{\text{AD}} + \overrightarrow{\text{CB}} + \overrightarrow{\text{DC}} =\]
\[= \left( \overrightarrow{\text{AD}} + \overrightarrow{\text{DC}} \right) + \overrightarrow{\text{CB}} = \overrightarrow{\text{AC}} + \overrightarrow{\text{CB}} =\]
\[= \overrightarrow{\text{AB}}.\]
\[\textbf{в)}\ \overrightarrow{\text{AB}} + \overrightarrow{\text{CD}} + \overrightarrow{\text{BC}} + \overrightarrow{\text{DA}} =\]
\[= \left( \overrightarrow{\text{AB}} + \overrightarrow{\text{BC}} \right) + \left( \overrightarrow{\text{CD}} + \overrightarrow{\text{DA}} \right) =\]
\[= \overrightarrow{\text{AC}} + \overrightarrow{\text{CA}} = \overrightarrow{\text{AA}} = \overrightarrow{0}.\]
