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Консультация № 194224
18.12.2018, 01:11
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Здравствуйте! Прошу помощи в следующем вопросе:
найти проекцию точки А (6,-8,-4)на плоскость проходящую через прямые ,
X= 2t+ 5
У= -13t+ 8
Z= 10t - 3
и
x= 11t + 7
у = 2t - 5
z= - 2t + 7
найти проекцию точки А (6,-8,-4)на плоскость проходящую через прямые ,
X= 2t+ 5
У= -13t+ 8
Z= 10t - 3
и
x= 11t + 7
у = 2t - 5
z= - 2t + 7
Обсуждение
19.12.2018, 16:05
общий
Цифры какие-то ненормальные получаются , но делал два раза с различными точками
Прикрепленные файлы:
21.12.2018, 09:17
общий
это ответ
Здравствуйте, lenocvol!
Из параметрических уравнений заданных прямых получим их канонические уравнения
и точку их пересечения
Векторы 
и 
являются для заданных прямых направляющими.
Вычислим координаты нормального вектора
заданной плоскости; получим
Выведем общее уравнение заданной плоскости; получим
Выведем канонические уравнения прямой, проходящей через заданную точку перпендикулярно к заданной плоскости; получим
Тогда уравнения двух пересекающихся плоскостей имеют вид
или
Присоединив к двум последним уравнениям общее уравнение заданной плоскости, получим систему трёх линейных уравнений с тремя неизвестными
-- координатами искомой проекции:
Решив эту систему уравнений в MS Excel по формулам Крамера (в прикреплённом файле), получим
Из параметрических уравнений заданных прямых получим их канонические уравнения
и точку их пересечения
Векторы и являются для заданных прямых направляющими.Вычислим координаты нормального вектора
заданной плоскости; получимВыведем общее уравнение заданной плоскости; получим
Выведем канонические уравнения прямой, проходящей через заданную точку перпендикулярно к заданной плоскости; получим
Тогда уравнения двух пересекающихся плоскостей имеют вид
или
Присоединив к двум последним уравнениям общее уравнение заданной плоскости, получим систему трёх линейных уравнений с тремя неизвестными
-- координатами искомой проекции:Решив эту систему уравнений в MS Excel по формулам Крамера (в прикреплённом файле), получим
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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