Bush Greene
05/01/2023 · Junior High School
№ 1. Даны векторы \( \vec{a}=(3 ;-5 ; 1), \vec{b}=(6 ; 2 ;-2) \) 1. Найти координаты векторов: \( -2 \vec{a}, \vec{a}+\vec{b}, \vec{a}-\vec{b} \) 2. Построить векторы: \( \vec{a}, \vec{b},-2 \vec{a}, \vec{a}+\vec{b}, \vec{a}-\vec{b} \) 3. Найти длину векторов: \( |\vec{a}|,|\vec{b}|,|-2 \vec{a}|,|\vec{a}+\vec{b}|,|\vec{a}-\vec{b}| \) № 2.
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1. Векторы: \( -2 \vec{a} = (-6, 10, -2) \), \( \vec{a} + \vec{b} = (9, -3, -1) \), \( \vec{a} - \vec{b} = (-3, -7, 3) \).
2. Векторы можно построить в трёхмерной системе координат.
3. Длины векторов: \( |\vec{a}| = \sqrt{35} \), \( |\vec{b}| = 2\sqrt{11} \), \( |-2 \vec{a}| = 2\sqrt{35} \), \( |\vec{a} + \vec{b}| = \sqrt{91} \), \( |\vec{a} - \vec{b}| = \sqrt{67} \).
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