Решебник по геометрии 11 класс. Атанасян ФГОС 752

\[\boxed{\mathbf{752.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]

\[\textbf{а)}\ \overrightarrow{\text{AB}}\left\{ 1;1; - 2 \right\};\ \ \overrightarrow{\text{CD}}\left\{ - 3;3; - 1 \right\}:\]

\[\cos{\angle\left( \overrightarrow{\text{AB}};\overrightarrow{\text{CD}} \right)} =\]

\[= \frac{|2|}{\sqrt{1 + 1 + 4} \cdot \sqrt{9 + 9 + 1}} =\]

\[= \frac{2}{\sqrt{114}}.\]

\[\textbf{б)}\ \overrightarrow{\text{AB}}\left\{ - 5;1;1 \right\};\ \ \overrightarrow{\text{CD}}\left\{ 2;2; - 2 \right\}:\]

\[\cos{\angle\left( \overrightarrow{\text{AB}};\overrightarrow{\text{CD}} \right)} =\]

\[= \frac{| - 10 + 2 - 2|}{\sqrt{25 + 1 + 1} \cdot \sqrt{4 + 4 + 4}} =\]

\[= \frac{10}{3\sqrt{3} \cdot 2\sqrt{3}} = \frac{10}{18} = \frac{5}{9}.\]