ГДЗ по геометрии 8 класс Атанасян Задание 1047

\[\boxed{\mathbf{1047.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\mathbf{Дано:}\ \]

\[\overrightarrow{a}\ и\ \overrightarrow{b}.\]

\[Найти:\]

\[x,\ при\ котором\ \overrightarrow{a}\bot\overrightarrow{b}.\]

\[Решение:\]

\[Если\ \overrightarrow{a}\bot\overrightarrow{b},\ то\ должно\ \]

\[выполнять\ условие:\]

\[\overrightarrow{a} \bullet \overrightarrow{b} = 0.\]

\[\textbf{а)}\ \overrightarrow{a}\left\{ 4;5 \right\};\ \overrightarrow{b}\left\{ x; - 6 \right\}:\]

\[\overrightarrow{a} \bullet \overrightarrow{b} = 4x + 5 \bullet ( - 6) = 0\]

\[4x - 30 = 0\]

\[x = 7,5.\]

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

\[\overrightarrow{a} \bullet \overrightarrow{b} = x \bullet 3 + ( - 1) \bullet 2 = 0\]

\[3x - 2 = 0\]

\[x = \frac{2}{3}.\]

\[\textbf{в)}\ \overrightarrow{a}\left\{ 0; - 3 \right\};\ \overrightarrow{b}\left\{ 5;x \right\}:\]

\[\overrightarrow{a} \bullet \overrightarrow{b} = 0 \bullet 5 + ( - 3)x = 0\]

\[- 3x = 0\]

\[x = 0.\]