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Консультация № 194302
26.12.2018, 13:25
0.00 руб.
0
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Даны координаты вершин пирамиды А(10, 2,-1), В(4,-5,-3), С(8,3,5), D(0, 1, 8).
Найти основание K высоты, опущенной из вершины D на грань АВС.
Даны координаты вершин пирамиды А(10, 2,-1), В(4,-5,-3), С(8,3,5), D(0, 1, 8).
Найти основание K высоты, опущенной из вершины D на грань АВС.
Обсуждение
29.12.2018, 21:58
общий
это ответ
Здравствуйте, Valeriya!
Имеем
Вектор
а с ним и коллинеарный ему вектор 
являются нормальными векторами плоскости 
Поскольку точка 
расположена в этой плоскости, постольку получим
-- общее уравнение плоскости
Вектор является направляющим вектором прямой, проходящей через точку 
перпендикулярно плоскости Поэтому
-- канонические уравнения высоты, опущенной из вершины пирамиды на грань
От канонических уравнений высоты перейдём к уравнениям двух плоскостей, пересечением которых эта высота является. Получим
Решим систему двух последних уравнений и общего уравнения плоскости Получим
Имеем
Вектор
а с ним и коллинеарный ему вектор являются нормальными векторами плоскости Поскольку точка расположена в этой плоскости, постольку получим -- общее уравнение плоскости Вектор
является направляющим вектором прямой, проходящей через точку перпендикулярно плоскости Поэтому -- канонические уравнения высоты, опущенной из вершины пирамиды на грань От канонических уравнений высоты перейдём к уравнениям двух плоскостей, пересечением которых эта высота является. Получим
Решим систему двух последних уравнений и общего уравнения плоскости
Получим
5
Об авторе:
Facta loquuntur.
Facta loquuntur.
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