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Консультация № 194681
12.02.2019, 07:40
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Объясните, как найти расстояние от точки (1, 2, 3) до прямой
(х-2)/1 = (у+3)/2 = (z+4)/3
Большое спасибо
Объясните, как найти расстояние от точки (1, 2, 3) до прямой
(х-2)/1 = (у+3)/2 = (z+4)/3
Большое спасибо
Обсуждение
12.02.2019, 08:50
общий
это ответ
Здравствуйте, Лилия!
Из уравнения заданной прямой видно, что вектор
является направляющим вектором этой прямой и нормальным вектором плоскости, перпендикулярного к этой прямой. Эта плоскость проецирует заданную точку на заданную прямую; общее уравнение этой плоскости суть
(коэффициенты перед скобками -- это координаты указанного выше вектора, а числа в скобках -- это координаты заданной точки), или
Чтобы вычислить координаты проекции заданной точки на заданную прямую, составим и решим систему уравнений, определяющую координаты точки пересечения заданной прямой и плоскости, общее уравнение которой указано выше. Получим
(решение системы по формулам Крамера находится в прикреплённом файле).
Следовательно, расстояние между заданной точкой и её проекцией на заданную прямую, равное искомому расстоянию, составляет
(ед. длины).
Из уравнения заданной прямой видно, что вектор
является направляющим вектором этой прямой и нормальным вектором плоскости, перпендикулярного к этой прямой. Эта плоскость проецирует заданную точку на заданную прямую; общее уравнение этой плоскости суть(коэффициенты перед скобками -- это координаты указанного выше вектора, а числа в скобках -- это координаты заданной точки), или
Чтобы вычислить координаты проекции заданной точки на заданную прямую, составим и решим систему уравнений, определяющую координаты точки пересечения заданной прямой и плоскости, общее уравнение которой указано выше. Получим
(решение системы по формулам Крамера находится в прикреплённом файле).
Следовательно, расстояние между заданной точкой и её проекцией на заданную прямую, равное искомому расстоянию, составляет
(ед. длины).
Прикрепленные файлы:
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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