\[\boxed{\mathbf{988.ОК\ ГДЗ - домашка\ на}\ 5}\]
\[Дано:\ \]
\[\overrightarrow{a}\ и\ \overrightarrow{b}\ не\ коллинеарны.\]
\[Найти:\]
\[x,\ чтобы\ \overrightarrow{p}\ и\ \overrightarrow{q} - коллинеарны.\]
\[Решение.\]
\[\textbf{а)}\ \overrightarrow{p} = 2\overrightarrow{a} - \overrightarrow{b};\ \ \ \overrightarrow{q} = \overrightarrow{a} + x\overrightarrow{b}:\]
\[\frac{2}{1} = - \frac{1}{x}\]
\[2x = - 1\]
\[x = - \frac{1}{2}.\]
\[\textbf{б)}\ \overrightarrow{p} = x\overrightarrow{a} - \overrightarrow{b};\ \ \ \overrightarrow{q} = \overrightarrow{a} + x\overrightarrow{b}:\]
\[\frac{x}{1} = - \frac{1}{x}\]
\[x^{2} = - 1 - нет\ решений;\]
\[\ \overrightarrow{p}\ и\ \overrightarrow{q}\ не\ коллинеарны.\]
\[\textbf{в)}\ \overrightarrow{p} = \overrightarrow{a} + x\overrightarrow{b};\ \ \ \overrightarrow{q} = \overrightarrow{a} - 2\overrightarrow{b}:\]
\[\frac{1}{1} = - \frac{x}{2}\]
\[x = - 2.\]
\[\textbf{г)}\ \overrightarrow{p} = 2\overrightarrow{a} + \overrightarrow{b};\ \ \ \overrightarrow{q} = \overrightarrow{\text{xa}} + \overrightarrow{b}:\]
\[\frac{2}{x} = \frac{1}{1}\]
\[2 = x\]
\[x = 2.\]