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Консультация № 191220
12.07.2017, 11:43
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Даны координаты вершин треугольника АВС относительно декартовой системы координат:
A=(3,7,4), B=(2,5,2), C=(1,5,3).
Запишите каноническое и параметрическое уравнения прямой Z, на которой расположена биссектриса AК треугольника АВС.
В ответ введите координаты точки Р пересечения прямой Z с плоскостью z=-8, разделив их точкой с запятой.
A=(3,7,4), B=(2,5,2), C=(1,5,3).
Запишите каноническое и параметрическое уравнения прямой Z, на которой расположена биссектриса AК треугольника АВС.
В ответ введите координаты точки Р пересечения прямой Z с плоскостью z=-8, разделив их точкой с запятой.
Обсуждение
12.07.2017, 14:36
общий
это ответ
Здравствуйте, Dmitry!
Пусть даны точки
Тогда
то есть в треугольнике
боковые стороны 
и 
имеют одинаковые длины; биссектриса, проведённая из вершины угла 
является медианой. Координаты середины отрезка 
суть
Прямая
проходит через середину отрезка и точку 
поэтому её направляющий вектор имеет координаты
В качестве направляющего удобнее принять противоположно направленный вектор
тогда канонические уравнения прямой суть
а параметрические - суть
или
Если
то 
Следовательно, прямая пересекается с плоскостью 
в точке 
Пусть даны точки
Тогдато есть в треугольнике
боковые стороны и имеют одинаковые длины; биссектриса, проведённая из вершины угла является медианой. Координаты середины отрезка сутьПрямая
проходит через середину отрезка и точку поэтому её направляющий вектор имеет координатыВ качестве направляющего удобнее принять противоположно направленный вектор
тогда канонические уравнения прямой
сутьа параметрические - суть
или
Если
то Следовательно, прямая пересекается с плоскостью в точке
Об авторе:
Facta loquuntur.
Facta loquuntur.
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