Решебник по геометрии 10 класс Атанасян ФГОС 664

\[\boxed{\mathbf{664.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]

\[Формула:\]

\[\textbf{а)}\ \overrightarrow{a}\left\{ 5; - 1;7 \right\}:\]

\[\left| \overrightarrow{a} \right| = \sqrt{5^{2} + ( - {1)}^{2} + 7^{2}} = \sqrt{75} =\]

\[= 5\sqrt{3}.\]

\[\textbf{б)}\ \overrightarrow{b}\left\{ 2\sqrt{3}; - 6;1 \right\}:\]

\[\left| \overrightarrow{b} \right| = \sqrt{\left( 2\sqrt{3} \right)^{2} + ( - 6)^{2} + 1^{2}} =\]

\[= \sqrt{49} = 7.\]

\[\textbf{в)}\ \overrightarrow{c} = \overrightarrow{i} + \overrightarrow{j} + \overrightarrow{k}:\]

\[\left| \overrightarrow{c} \right| = \sqrt{1^{2} + 1^{2} + 1^{2}} = \sqrt{3}.\]

\[\textbf{г)}\ \overrightarrow{d} = - 2\overrightarrow{k}:\]

\[\left| \overrightarrow{d} \right| = \sqrt{0^{2} + 0^{2} + ( - 2)^{2}} = 2.\]

\[\textbf{д)}\ \overrightarrow{m} = \overrightarrow{i} - 2\overrightarrow{j}:\]

\[\left| \overrightarrow{m} \right| = \sqrt{1^{2} + ( - 2)^{2} + 0^{2}} = \sqrt{5}.\]