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МатематикаРешебник по геометрии 11 класс. Атанасян ФГОС 576
576
\[\boxed{\mathbf{576.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]
\[Дано:\]
\[Найти:\]
\[вектор\ \overrightarrow{x}.\]
\[Решение.\]
\[\textbf{а)}\ \overrightarrow{\text{DC}} + \overrightarrow{D_{1}A_{1}} + \overrightarrow{CD_{1}} + \overrightarrow{x} + \overrightarrow{A_{1}C_{1}} =\]
\[= \overrightarrow{\text{DB}}\]
\[\left( \overrightarrow{\text{DC}} + \overrightarrow{CD_{1}} + \overrightarrow{D_{1}A_{1}} + \overrightarrow{A_{1}C_{1}} \right) + \overrightarrow{x} =\]
\[= \overrightarrow{\text{DB}}\]
\[\overrightarrow{DC_{1}} + \overrightarrow{x} = \overrightarrow{\text{DB}}\]
\[\overrightarrow{x} = \overrightarrow{\text{DB}} - \overrightarrow{DC_{1}} = \overrightarrow{C_{1}D} + \overrightarrow{\text{DB}} =\]
\[= \overrightarrow{C_{1}B}.\]
\[\textbf{б)}\ \overrightarrow{\text{DA}} + \overrightarrow{x} + \overrightarrow{D_{1}B} + \overrightarrow{AD_{1}} + \overrightarrow{\text{BA}} =\]
\[= \overrightarrow{\text{DC}}\]
\[\left( \overrightarrow{\text{DA}} + \overrightarrow{AD_{1}} + \overrightarrow{D_{1}B} + \overrightarrow{\text{BA}} \right) + \overrightarrow{x} =\]
\[= \overrightarrow{\text{DC}}\]
\[\overrightarrow{\text{DA}} + \overrightarrow{x} = \overrightarrow{\text{DC}}\]
\[\overrightarrow{x} = \overrightarrow{\text{DC}} - \overrightarrow{\text{DA}} = \overrightarrow{\text{AD}} + \overrightarrow{\text{DC}} = \overrightarrow{\text{AC}}.\]
\[Ответ:\ \ а)\ \overrightarrow{C_{1}B};\ \ б)\ \overrightarrow{\text{AC}}.\]
