Решебник по геометрии 11 класс. Атанасян ФГОС 694

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\[A(1;3;0);\ \ B(2;3; - 1);\ \ \]

\[C(1;2; - 1).\]

\[\overrightarrow{\text{CA}}\left\{ 0;1;1 \right\};\ \ \ \overrightarrow{\text{CB}}\left\{ 1;1;0 \right\}.\]

\[\cos{\angle\left( \overrightarrow{\text{CA}};\overrightarrow{\text{CB}} \right)} =\]

\[= \frac{0 + 1 + 0}{\sqrt{1^{2} + 1^{2}} \cdot \sqrt{1^{2} + 1^{2}}} =\]

\[= \frac{1}{\sqrt{2} \cdot \sqrt{2}} = \frac{1}{2};\]

\[\angle\left( \overrightarrow{\text{CA}};\overrightarrow{\text{CB}} \right) = 60{^\circ}.\]

\[Ответ:60{^\circ}.\]