ГДЗ по геометрии 11 класс. Атанасян ФГОС 596

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\[\textbf{а)}\ По\ правилу\ \]

\[параллелепипеда:\]

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

\[\textbf{б)}\ По\ правилу\ треугольника:\]

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

\[B_{1}B \parallel A_{1}A;\ \ \ B_{1}B = A_{1}A:\]

\[\overrightarrow{B_{1}A_{1}} + \overrightarrow{A_{1}B} = \overrightarrow{B_{1}B} = \overrightarrow{A_{1}A}\text{.\ }\]

\[Отсюда:\ \]

\[\overrightarrow{B_{1}A_{1}} = \overrightarrow{A_{1}A} - \overrightarrow{A_{1}B};\]

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