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Консультация № 189295
03.05.2016, 18:24
0.00 руб.
0
1
1
Здравствуйте, уважаемые эксперты! У меня возникли сложности с таким вопросом:
написать уравнение плоскости, проходящей через точки М (0;1;1) и N (2;0;1) перпендикулярно плоскости 2х-у+z+1=0.
У меня получился ответ 0,5х+у-1,5z+0,5=0, но, наверное, это неправильно, я ничего не понял.
написать уравнение плоскости, проходящей через точки М (0;1;1) и N (2;0;1) перпендикулярно плоскости 2х-у+z+1=0.
У меня получился ответ 0,5х+у-1,5z+0,5=0, но, наверное, это неправильно, я ничего не понял.
Обсуждение
03.05.2016, 19:36
общий
это ответ
Здравствуйте, toph_bf!
Нормальным к плоскости, заданной общим уравнением
является вектор 
Этот вектор параллелен плоскости, уравнение которой нужно вывести. Пусть искомой плоскости принадлежит точка 
Тогда вектор 
образован соответственными координатами двух точек, принадлежащих искомой плоскости, и лежит в этой плоскости. То же относится и к вектору 
Смешанное произведение этих векторов (они компланарны) равно нулю, то есть
или
Это и есть ответ к задаче.
С уважением.
Нормальным к плоскости, заданной общим уравнением
является вектор Этот вектор параллелен плоскости, уравнение которой нужно вывести. Пусть искомой плоскости принадлежит точка Тогда вектор образован соответственными координатами двух точек, принадлежащих искомой плоскости, и лежит в этой плоскости. То же относится и к вектору Смешанное произведение этих векторов (они компланарны) равно нулю, то естьили
Это и есть ответ к задаче.
С уважением.
5
Большое спасибо за развёрнутый ответ!
Об авторе:
Facta loquuntur.
Facta loquuntur.
Форма ответа
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