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

Решение: 1. Найдем вектор 3\(\vec{a}\): 3\(\vec{a}\) = 3 * (2\(\vec{i}\) - 3\(\vec{j}\)) = 6\(\vec{i}\) - 9\(\vec{j}\) 2. Найдем вектор 2\(\vec{b}\): 2\(\vec{b}\) = 2 * (4\(\vec{i}\) + 5\(\vec{j}\)) = 8\(\vec{i}\) + 10\(\vec{j}\) 3. Найдем вектор 3\(\vec{a}\) - 2\(\vec{b}\): 3\(\vec{a}\) - 2\(\vec{b}\) = (6\(\vec{i}\) - 9\(\vec{j}\)) - (8\(\vec{i}\) + 10\(\vec{j}\)) = -2\(\vec{i}\) - 19\(\vec{j}\) 4. Найдем модуль вектора 3\(\vec{a}\) - 2\(\vec{b}\): |3\(\vec{a}\) - 2\(\vec{b}\)| = \(\sqrt{(-2)^2 + (-19)^2}\) = \(\sqrt{4 + 361}\) = \(\sqrt{365}\) Ответ: \(\sqrt{365}\)