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Два вектора в евклидовом пространстве ортогональны. Чему равно их скалярное произведение.

Ask by Lambert Hodgson. in Russia
Feb 24,2025

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Answer

Скалярное произведение ортогональных векторов равно 0.

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Если два вектора в евклидовом пространстве ортогональны (то есть перпендикулярны), их скалярное произведение равно 0.

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Если два вектора в евклидова пространстве ортогональны, это означает, что угол между ними равен 90 градусам. В таком случае их скалярное произведение равно нулю. Это следует из определения скалярного произведения: оно выражается как произведение длины одного вектора на длину другого и косинус угла между ними. Поскольку косинус 90 градусов равен нулю, то и скалярное произведение векторов будет равно нулю. Еще один интересный факт: ортогональные вектора находят широкое применение в компьютерной графике и машинном обучении. Например, вектор нормали к поверхности часто ортогонален к вектору направлению света. Это облегчает расчеты, такие как освещение, и помогает правильно отображать объекты на экране.

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