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Консультация № 181323
13.12.2010, 19:22
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Здравствуйте, уважаемые эксперты! Прошу Вас ответить на следующий вопрос:
Задача на уравнение прямой и плоскости в пространстве:
Составить уравнение плоскости, проходящей через т. M0 (3;-2;-7) перпендикулярно к прямой x-2/3=y-3/2=z+7/-3
Задача на уравнение прямой и плоскости в пространстве:
Составить уравнение плоскости, проходящей через т. M0 (3;-2;-7) перпендикулярно к прямой x-2/3=y-3/2=z+7/-3
Обсуждение
13.12.2010, 19:54
общий
это ответ
Здравствуйте, Посетитель - 351624!
Вектор {3;2;-3} является направляющим вектором прямой, следовательно, он перпендикулярен искомой плоскости. Уравнение плоскости, проходящей через заданную точку M0(x0;y0;z0) с перпендикулярным вектором {A;B;C} имеет вид
A(x-x0)+B(y-y0)+C(z-z0)=0
Таким образом, искомое уравнение:
3(x-3)+2(y+2)-3(z+7)=0
или
3x+2y-3z-26=0
Вектор {3;2;-3} является направляющим вектором прямой, следовательно, он перпендикулярен искомой плоскости. Уравнение плоскости, проходящей через заданную точку M0(x0;y0;z0) с перпендикулярным вектором {A;B;C} имеет вид
A(x-x0)+B(y-y0)+C(z-z0)=0
Таким образом, искомое уравнение:
3(x-3)+2(y+2)-3(z+7)=0
или
3x+2y-3z-26=0
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