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Линал. шпора лин ал. 1. Сложение матриц, умножение матрицы на число, умножение матриц. Транспонирование матриц. Основные свойства этих операций. Сложение
18.Прямая и плоскости в пространстве. Их взаимное расположение. Расстояние от точки до плоскости.
Уравнение A(x-x0)+B(X-X0)+C(X-X0)=0 определяет плоскость, проходящую через точку М(x0,y0,z0) и имеющую нормальный вектор n(A,B,C)
Расстояние от плоскости до точки:
![](data:image/png;base64,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)
Пусть плоскости заданы общими уравнениями:
P1: A1X+B1Y+C1Z+D=0 P2: A2X+B2Y+C2Z+D=0 . Тогда:
1) если A1/A2=B1/B2=C1/C2=D1/D2 то плоскости совпадают;
2) если A1/A2=B1/B2=C1/C2 не равно D1/D2 то плоскости параллельные;
3) если или, то плоскости пересекаются по прямой, уравнением которой служит система уравнений:
A1/A2не равноB1/B2 или B1/B2не равно C1/C2
Угол между прямой и плоскостью:
![](data:image/png;base64,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)
1. Прямая параллельна плоскости, если она не имеет с плоскостью общих точек.
![](data:image/png;base64,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)
2. Прямая пересекает плоскость, если она имеет с плоскостью ровно одну общую точку.
![](data:image/png;base64,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)
3. Прямая лежит в плоскости, если каждая точка прямой принадлежит этой плоскости.
![](data:image/png;base64,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)
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