Решебник по геометрии 10 класс Атанасян ФГОС 630

\[\boxed{\mathbf{630.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]

\[Дано:\ \]

\[\text{ABCD}A_{1}B_{1}C_{1}D_{1} -\]

\[параллелепипед;\ \ \]

\[CK = KC_{1}.\]

\[Решение.\]

\[\textbf{а)}\ \overrightarrow{\text{AK}} = \overrightarrow{\text{AB}} + \overrightarrow{\text{BC}} + \overrightarrow{\text{CK}} =\]

\[= \overrightarrow{\text{AB}} + \overrightarrow{\text{AD}} + \frac{1}{2}\overrightarrow{CC_{1}} =\]

\[= \overrightarrow{\text{AB}} + \overrightarrow{\text{AD}} + \frac{1}{2}\overrightarrow{AA_{1}}.\]

\[\textbf{б)}\ \overrightarrow{DA_{1}} = \overrightarrow{DC_{1}} + \overrightarrow{C_{1}B} + \overrightarrow{BA_{1}} =\]

\[= \overrightarrow{AB_{1}} - \overrightarrow{BC_{1}} + \overrightarrow{CD_{1}}.\]