Решебник по геометрии 10 класс Атанасян ФГОС 595

\[\boxed{\mathbf{595.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]

\[Для\ сложения\ векторов,\ \]

\[воспользуемся\ правилом\ \]

\[параллелепипеда.\]

\[\textbf{а)}\ \overrightarrow{\text{AB}} + \overrightarrow{\text{AD}} + \overrightarrow{AA_{1}} = \overrightarrow{AC_{1}}.\]

\[\textbf{б)}\ \overrightarrow{\text{DA}} + \overrightarrow{\text{DC}} + \overrightarrow{DD_{1}} = \overrightarrow{DB_{1}}.\]

\[\textbf{в)}\ \overrightarrow{A_{1}B_{1}} = \overrightarrow{\text{DC}};\ \ \overrightarrow{C_{1}B_{1}} = \overrightarrow{\text{DA}};\ \ \]

\[\overrightarrow{BB_{1}} = \overrightarrow{DD_{1}}:\]

\[\overrightarrow{A_{1}B_{1}} + \overrightarrow{C_{1}B_{1}} + \overrightarrow{BB_{1}} =\]

\[= \overrightarrow{\text{DC}} + \overrightarrow{\text{DA}} + \overrightarrow{DD_{1}} = \overrightarrow{DB_{1}}.\]

\[\textbf{г)}\ \overrightarrow{\text{AB}} = \overrightarrow{A_{1}B_{1}}:\]

\[\overrightarrow{A_{1}A} + \overrightarrow{A_{1}D_{1}} + \overrightarrow{\text{AB}} =\]

\[= \overrightarrow{A_{1}A} + \overrightarrow{A_{1}D_{1}} + \overrightarrow{A_{1}B_{1}} = \overrightarrow{A_{1}C}.\]

\[\textbf{д)}\ \overrightarrow{B_{1}A_{1}} = \overrightarrow{\text{BA}}:\]

\[\overrightarrow{B_{1}A_{1}} + \overrightarrow{BB_{1}} + \overrightarrow{\text{BC}} =\]

\[= \overrightarrow{\text{BA}} + \overrightarrow{BB_{1}} + \overrightarrow{\text{BC}} = \overrightarrow{BD_{1}}.\]