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Консультация № 193849
08.11.2018, 19:56
0.00 руб.
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2
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Для прямых 2х - 4у + 1 = 0 и 3х + 4у + 5= 0 найти их взаимное расположение. В случае их пересечения найти угол между ними, в случае их параллельности - расстояние
Для прямых 2х - 4у + 1 = 0 и 3х + 4у + 5= 0 найти их взаимное расположение. В случае их пересечения найти угол между ними, в случае их параллельности - расстояние
Обсуждение
08.11.2018, 20:04
общий
Адресаты:
Вы можете самостоятельно решить эту систему уравнений?
Об авторе:
Facta loquuntur.
Facta loquuntur.
08.11.2018, 22:29
общий
это ответ
Здравствуйте, li.a!
Решая систему уравнений
определяющих заданные прямые, получим, что прямые пересекаются в точке
Обе прямые заданы своими общими уравнениями. Из этих уравнений следует, что нормальными векторами первой и второй прямой соответственно являются векторы
и 
Вычисление угла между этими прямыми можно свести к вычислению угла между их нормальными векторами. Получим
Полученный результат свидетельствует о том, что для совмещения направления вектора
с направлением вектора 
нужно повернуть первый вектор в направлении против хода часовой стрелки на угол, приблизительно равный 
или вектор 
повернуть в направлении по ходу часовой стрелки на угол, приблизительно равный 
Эти два угла (без указания направления вращения) образуются и при пересечении заданных прямых.
Решая систему уравнений
определяющих заданные прямые, получим, что прямые пересекаются в точке
Обе прямые заданы своими общими уравнениями. Из этих уравнений следует, что нормальными векторами первой и второй прямой соответственно являются векторы
и Вычисление угла между этими прямыми можно свести к вычислению угла между их нормальными векторами. ПолучимПолученный результат свидетельствует о том, что для совмещения направления вектора
с направлением вектора нужно повернуть первый вектор в направлении против хода часовой стрелки на угол, приблизительно равный или вектор повернуть в направлении по ходу часовой стрелки на угол, приблизительно равный Эти два угла (без указания направления вращения) образуются и при пересечении заданных прямых.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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