Решебник по геометрии 10 класс Атанасян ФГОС 749

\[\boxed{\mathbf{749.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]

\[\overrightarrow{a}\left\{ - 1;5;3 \right\};\ \ \overrightarrow{b}\left\{ 3;0;2 \right\};\ \ \]

\[\overrightarrow{c}\left\{ 0,5; - 3;4 \right\};\ \ \overrightarrow{d}\left\{ 2;1;0 \right\}.\]

\[\textbf{а)}\ \overrightarrow{a}\overrightarrow{b} = - 1 \cdot 3 + 5 \cdot 0 + 3 \cdot 2 = 3.\]

\[\textbf{б)}\ \overrightarrow{a}\overrightarrow{c} = - 1 \cdot \frac{1}{2} - 3 \cdot 5 + 3 \cdot 4 =\]

\[= - \frac{1}{2} - 3 = - 3,5.\]

\[\textbf{в)}\ \overrightarrow{d}\overrightarrow{d} = 2^{2} + 1^{2} + 0^{2} = 5.\]

\[\textbf{г)}\ \left( \overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} \right)\overrightarrow{d} =\]

\[= \overrightarrow{a}\overrightarrow{d} + \overrightarrow{b}\overrightarrow{d} + \overrightarrow{c}\overrightarrow{d} =\]

\[= 3 + 6 - 2 = 7.\]

\[\textbf{д)}\ \left( \overrightarrow{a} - \overrightarrow{b} \right)\left( \overrightarrow{c} - \overrightarrow{d} \right) =\]

\[= \overrightarrow{a}\overrightarrow{c} - \overrightarrow{b}\overrightarrow{c} - \overrightarrow{a}\overrightarrow{d} + \overrightarrow{b}\overrightarrow{d} =\]