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Консультация № 155047
20.12.2008, 03:40
0.00 руб.
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Здравствуйте! помогите пожалуста решить задачу=))
Даны вектора а=(1,-3,-4) , b=(8,-10,10), c=(-1,-1,-1). Найти вектор х, перпендикулярный a и b, такой что (х,с)=7
Даны вектора а=(1,-3,-4) , b=(8,-10,10), c=(-1,-1,-1). Найти вектор х, перпендикулярный a и b, такой что (х,с)=7
Обсуждение
Неизвестный
20.12.2008, 03:44
общий
Здравствуйте! Помогите решить задачку!=)))
Даны вектора a=(1,-3,-4) , b=(8,-10,-10), c=(-1,-1,-1). Найти вектор х перпендикулярный a и b, такой что (х,с)=7.
Заранее, спасибо!=)))
Даны вектора a=(1,-3,-4) , b=(8,-10,-10), c=(-1,-1,-1). Найти вектор х перпендикулярный a и b, такой что (х,с)=7.
Заранее, спасибо!=)))
Неизвестный
20.12.2008, 14:20
общий
это ответ
Здравствуйте, Namina!
Обозначим элементы вектора х за х1, х2 и х3.
Так как х перпендикулярен а и b, то (x,a) = 0, (x,b) = 0; добавив к этому выражение (x,c) = 7, получаем систему уравнений :
x1 - 3*x2 - 4*x3 = 0; 8*x1 - 10*x2 + 10*x3 = 0; -x1 - x2 - x3 =7
Из первого уравнения выразим х1: х1 = 3*х2 + 4*х3.
Подставим это во второе уравнение и выразим х2: х2 = -3*х3 => х1 = -5*х3.
Подставим два последних выражения в третье уравнение: х3 = 1 => x2 = -3 => x1 = -5.
Значит, вектор х = (-5, -3, 1)
Обозначим элементы вектора х за х1, х2 и х3.
Так как х перпендикулярен а и b, то (x,a) = 0, (x,b) = 0; добавив к этому выражение (x,c) = 7, получаем систему уравнений :
x1 - 3*x2 - 4*x3 = 0; 8*x1 - 10*x2 + 10*x3 = 0; -x1 - x2 - x3 =7
Из первого уравнения выразим х1: х1 = 3*х2 + 4*х3.
Подставим это во второе уравнение и выразим х2: х2 = -3*х3 => х1 = -5*х3.
Подставим два последних выражения в третье уравнение: х3 = 1 => x2 = -3 => x1 = -5.
Значит, вектор х = (-5, -3, 1)
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