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Консультация № 159672
05.02.2009, 12:53
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вашей помощи в решении следующих задач:
1. Даны векторы a, b, c и d. Показать, что векторы a, b, c образуют базис и найти координаты вектора d в этом базисе.
a (1, -1, 4), b (3, -2, -1), c (-2, 1, -1), d (5, -3, 6).
2. Даны координаты вершин пирамиды A1A2A3A4. Найти: а) угол между ребрами A1A2 и A1A3; б) площадь грани A1A2A3;
в) уравнение плоскости A1A2A3; г) уравнение высоты, проходящей через A4; д) объем пирамиды.
3. Привести уравнение кривой второго порядка к каконическому виду. Для эллипса найти координаты вершин и фокусов, для гиперболы - координаты вершин, фокусов и уравнения ассимптот, для параболы - координаты фокуса и уравнение директрисы, для окружности - координаты центра и радиус. Сделать чертеж.
(y-x)(x+y)=-4.
4. Написать уравнение касательной, проведенной к графику данной функции параллельно данной прямой. Если таких касательных две, привести уравнение только одной из них.
y=[$8730$]x; x-4y=4.
Заранее благодарю!
1. Даны векторы a, b, c и d. Показать, что векторы a, b, c образуют базис и найти координаты вектора d в этом базисе.
a (1, -1, 4), b (3, -2, -1), c (-2, 1, -1), d (5, -3, 6).
2. Даны координаты вершин пирамиды A1A2A3A4. Найти: а) угол между ребрами A1A2 и A1A3; б) площадь грани A1A2A3;
в) уравнение плоскости A1A2A3; г) уравнение высоты, проходящей через A4; д) объем пирамиды.
3. Привести уравнение кривой второго порядка к каконическому виду. Для эллипса найти координаты вершин и фокусов, для гиперболы - координаты вершин, фокусов и уравнения ассимптот, для параболы - координаты фокуса и уравнение директрисы, для окружности - координаты центра и радиус. Сделать чертеж.
(y-x)(x+y)=-4.
4. Написать уравнение касательной, проведенной к графику данной функции параллельно данной прямой. Если таких касательных две, привести уравнение только одной из них.
y=[$8730$]x; x-4y=4.
Заранее благодарю!
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