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Консультация № 199946
21.12.2020, 14:34
0.00 руб.
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Здравствуйте! У меня возникли сложности с таким вопросом:
"Найти точку пересечения прямой, заданной каноническими уравнениями, и плоскости (x+3/1)=(y-2/-5)=(z+2/3),
5x-y+4z+3=0." Скрин тоже есть.
"Найти точку пересечения прямой, заданной каноническими уравнениями, и плоскости (x+3/1)=(y-2/-5)=(z+2/3),
5x-y+4z+3=0." Скрин тоже есть.
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Обсуждение
12.07.2022, 13:11
общий
это ответ
Здравствуйте, Oleg!
Из канонических уравнений прямой и уравнения плоскости получим следующую систему трёх линейных уравнений с тремя неизвестными:
или 
Из первого уравнения последней системы получим, что
из второго уравнения получим, что 
и подставим в третье уравнение. Тогда
При этом
Значит, заданные прямая и плоскость пересекаются в точке 
Из канонических уравнений прямой и уравнения плоскости получим следующую систему трёх линейных уравнений с тремя неизвестными:
или Из первого уравнения последней системы получим, что
из второго уравнения получим, что и подставим в третье уравнение. ТогдаПри этом
Значит, заданные прямая и плоскость пересекаются в точке
Об авторе:
Facta loquuntur.
Facta loquuntur.
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