В1. Найдите величину |\(2\overrightarrow{a} - 3\overrightarrow{b}\)|, если \(\overrightarrow{a} = 3i + 2j\) и \(\overrightarrow{b} = 5i - 4j\).

В1. Дано: \(\overrightarrow{a} = 3i + 2j\), \(\overrightarrow{b} = 5i - 4j\). Найти: |\(2\overrightarrow{a} - 3\overrightarrow{b}\)|

\(2\overrightarrow{a}\) = 2 × (3i + 2j) = 6i + 4j

\(3\overrightarrow{b}\) = 3 × (5i - 4j) = 15i - 12j

\(2\overrightarrow{a} - 3\overrightarrow{b}\) = (6i + 4j) - (15i - 12j) = (6 - 15)i + (4 + 12)j = -9i + 16j

|\(2\overrightarrow{a} - 3\overrightarrow{b}\)| = \(\sqrt{(-9)^2 + 16^2}\) = \(\sqrt{81 + 256}\) = \(\sqrt{337}\)

Ответ: \(\sqrt{337}\)