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Консультация № 118066
12.01.2008, 01:31
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Помогите пожалуяста решить пример. Найти точку пересечения с осью Oz плоскости, проходящей через три точки А(-1,2,-3), В(1,4,-5), и С(2,-1,1).
Обсуждение
Неизвестный
12.01.2008, 02:59
общий
это ответ
Здравствуйте, Шлык Елена Павловна!
Уравнение плоскости, проходящей через точки A, B и C :
| x+1 y-2 z+3 |
| x-1 y-4 z+5 | = 0
| x-2 y+1 z-1 |
Пусть искомая точка (x0, y0, z0)
Поскольку она лежит на оси Oz, то x0=y0=0
Остается найти z0 из уравнения:
| 1 -2 z0+3 |
| -1 -4 z0+5 | = 0
| -2 1 z0-1 |
Прибавив ко второй строке первую, а к 3-ей удвоенную первую, получим:
| 1 -2 z0+3 |
| 0 -6 2*z0+8 | = 0
| 0 -3 3*z0+5 |
А теперь из третьей вычтем половину второй. Имеем:
| 1 -2 z0+3 |
| 0 -6 2*z0+8 | = 0
| 0 0 2*z0+1 |
Отсюда получаем -6*( 2*z0 + 1 ) = 0 и z0 = -½
И, окончательно, искомая точка ( 0 , 0 , -½ ) .
Уравнение плоскости, проходящей через точки A, B и C :
| x+1 y-2 z+3 |
| x-1 y-4 z+5 | = 0
| x-2 y+1 z-1 |
Пусть искомая точка (x0, y0, z0)
Поскольку она лежит на оси Oz, то x0=y0=0
Остается найти z0 из уравнения:
| 1 -2 z0+3 |
| -1 -4 z0+5 | = 0
| -2 1 z0-1 |
Прибавив ко второй строке первую, а к 3-ей удвоенную первую, получим:
| 1 -2 z0+3 |
| 0 -6 2*z0+8 | = 0
| 0 -3 3*z0+5 |
А теперь из третьей вычтем половину второй. Имеем:
| 1 -2 z0+3 |
| 0 -6 2*z0+8 | = 0
| 0 0 2*z0+1 |
Отсюда получаем -6*( 2*z0 + 1 ) = 0 и z0 = -½
И, окончательно, искомая точка ( 0 , 0 , -½ ) .
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