ГДЗ по геометрии 7 класс Атанасян Задание 1068

\[\boxed{\mathbf{1068.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\mathbf{Дано:}\]

\[\left| \overrightarrow{a} \right| = 2;\]

\[\left| \overrightarrow{b} \right| = 5;\]

\[\widehat{\overrightarrow{a}\overrightarrow{b}} = 120{^\circ};\]

\[\overrightarrow{p} = x\overrightarrow{a} + 17\overrightarrow{b};\]

\[\overrightarrow{q} = 3\overrightarrow{a} - \overrightarrow{b};\]

\[\overrightarrow{p}\bot\overrightarrow{q}.\]

\[\mathbf{Найти:}\]

\[x - ?\]

\[\mathbf{Решение.}\]

\[1)\ \overrightarrow{p} \bullet \overrightarrow{q} =\]

\[= \left( x\overrightarrow{a} + 17\overrightarrow{b} \right)\left( 3\overrightarrow{a} - \overrightarrow{b} \right) =\]

\[= 3x{\overrightarrow{a}}^{2} - x\overrightarrow{a}\overrightarrow{b} + 51\overrightarrow{a}\overrightarrow{b} - 17{\overrightarrow{b}}^{2} =\]

\[= 12x + 5x - 225 - 425 =\]

\[= 17x - 680.\]

\[2)\ \overrightarrow{p}\bot\overrightarrow{q} \Longrightarrow \overrightarrow{p} \bullet \overrightarrow{q} = 0:\]

\[17x - 680 = 0\]

\[x = \frac{680}{17} = 40.\]

\[Ответ:\ x = 40.\]