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Консультация № 194502
23.01.2019, 21:15
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Даны вершины треугольной пирамиды
А(-9,-10,7), B(-2,5,-9), С(-2,-2,4), D(-2,-4,-7).
Найти:
1) длину ребра AD
2) объем пирамиды ABCD
3) угол альфа между ребрами АС и AD
4) уравнение плоскости BCD
5) уравнение прямой AC
6) острый угол бета между ребром AD и гранью ABC
7) уравнение высоты, опущенной из вершины D на грань ABC
Даны вершины треугольной пирамиды
А(-9,-10,7), B(-2,5,-9), С(-2,-2,4), D(-2,-4,-7).
Найти:
1) длину ребра AD
2) объем пирамиды ABCD
3) угол альфа между ребрами АС и AD
4) уравнение плоскости BCD
5) уравнение прямой AC
6) острый угол бета между ребром AD и гранью ABC
7) уравнение высоты, опущенной из вершины D на грань ABC
Обсуждение
27.01.2019, 09:09
общий
это ответ
Здравствуйте, roma5890!
1)
(ед. длины).
2)
(ед. объёма).
3)
4) Пусть
Тогда векторы 
компланарны. Значит,
-- общее уравнение плоскости 
Можно поступить проще: заметив, что абсциссы точек
равны 
сделать вывод о том, что 
или -- искомое уравнение.
5) Прямая
проходит через точку 
и 
-- её направляющий вектор. Поэтому
-- канонические уравнения прямой 
6)
-- нормальный вектор плоскости 
7) Вектор
-- направляющий вектор высоты, опущенной из вершины 
на грань 
Поэтому
-- канонические уравнения этой высоты,
-- уравнения этой высоты, заданной как пересечение плоскостей.
1)
(ед. длины).2)
(ед. объёма).3)
4) Пусть
Тогда векторы компланарны. Значит, -- общее уравнение плоскости Можно поступить проще: заметив, что абсциссы точек
равны сделать вывод о том, что или -- искомое уравнение.5) Прямая
проходит через точку и -- её направляющий вектор. Поэтому -- канонические уравнения прямой 6)
-- нормальный вектор плоскости 7) Вектор
-- направляющий вектор высоты, опущенной из вершины на грань Поэтому -- канонические уравнения этой высоты, -- уравнения этой высоты, заданной как пересечение плоскостей.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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