ГДЗ по геометрии 9 класс Атанасян Задание 1041

\[\boxed{\mathbf{1041.ОК\ ГДЗ - домашка\ на}\ 5}\]

\[\mathbf{Дано:}\]

\[\left| \overrightarrow{a} \right| = 2;\left| \overrightarrow{b} \right| = 3;\]

\[\textbf{а)}\ 45{^\circ};\]

\[\textbf{б)}\ 90{^\circ};\]

\[\textbf{в)}\ 135{^\circ}.\]

\[\mathbf{Найти:}\]

\[\overrightarrow{a} \bullet \overrightarrow{b} - ?\]

\[\mathbf{Решение.}\]

\[\ \overrightarrow{a} \bullet \overrightarrow{b} = \left| \overrightarrow{a} \right| \bullet \left| \overrightarrow{b} \right| \bullet \cos{(\widehat{\overrightarrow{a};\overrightarrow{b}}}).\]

\[\textbf{а)}\ \overrightarrow{a} \bullet \overrightarrow{b} = 2 \bullet 3 \bullet \cos{45{^\circ}} =\]

\[= 6 \bullet \frac{\sqrt{2}}{2} = 3\sqrt{2}.\]

\[\textbf{б)}\ \overrightarrow{a} \bullet \overrightarrow{b} = 2 \bullet 3 \bullet \cos{90{^\circ}} =\]

\[= 6 \bullet 0 = 0.\]

\[\textbf{в)}\ \overrightarrow{a} \bullet \overrightarrow{b} = 2 \bullet 3 \bullet \cos{135{^\circ}} =\]

\[= 6 \bullet \left( - \frac{\sqrt{2}}{2} \right) = - 3\sqrt{2}.\]