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Консультация № 190428
14.01.2017, 13:25
0.00 руб.
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Здравствуйте! Прошу помощи в следующем вопросе:
Через точку М провести прямые: параллельно, перпендикулярно к прямой l Сделать чертеж
Через точку М провести прямые: параллельно, перпендикулярно к прямой l Сделать чертеж
Прикрепленные файлы:
Обсуждение
15.01.2017, 10:36
общий
это ответ
Здравствуйте, Stofa!
Подставим в уравнение прямой
значение 
Получим 
Подставим в уравнение прямой значение 
Получим 
Прямая проходит через точки 
Из уравнения прямой
следует, что 
- её нормальный вектор, 
- её направляющий вектор. Приложим эти векторы к точке 
и проведём через точки этих векторов отрезки прямых. Получим результат, показанный на рисунке ниже. Прямая представлена отрезком 
Вектор 
и прямая, проходящая через точку 
перпендикулярно прямой 
представлены отрезком 
Вектор 
и прямая, проходящая через точку параллельно прямой представлены отрезком 
Разумеется, тот факт, что вместо векторов и к точке на рисунке приложены коллинеарные им отрезки, не влияет на результат.
Подставим в уравнение прямой
значение Получим Подставим в уравнение прямой значение Получим Прямая проходит через точки Из уравнения прямой
следует, что - её нормальный вектор, - её направляющий вектор. Приложим эти векторы к точке и проведём через точки этих векторов отрезки прямых. Получим результат, показанный на рисунке ниже. Прямая представлена отрезком Вектор и прямая, проходящая через точку перпендикулярно прямой представлены отрезком Вектор и прямая, проходящая через точку параллельно прямой представлены отрезком Разумеется, тот факт, что вместо векторов
и к точке на рисунке приложены коллинеарные им отрезки, не влияет на результат.
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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