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Консультация № 194127
08.12.2018, 00:56
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: при каком значении λ прямые l1 : (x−1)/4= (y+2)/-1= (z+4)/1 и l2 : (x−3) /3= (y−1)/1= (z−λ)/1 пересекаются? Найти точку пересечения.
Обсуждение
11.12.2018, 08:58
общий
это ответ
Здравствуйте, sasha181999_9!
Согласно заданию, направляющими векторами прямых являются
При этом точка
лежит на прямой 
а точка 
лежит на прямой 
Заданные прямые будут пересекаться, если выполнено условие
то есть векторы
компланарны (при этом их смешанное произведение равно нулю). Тогда
Вычислим координаты точки пересечения прямых
и 
Для этого перепишем уравнения прямых в параметрической форме; получим
Поскольку координаты
точки пересечения прямых должны удовлетворять обеим полученным системам уравнений, постольку приравнивая друг к другу соответствующие уравнения, получим
Следовательно, заданные прямые пересекаются в точке с координатами
Согласно заданию, направляющими векторами прямых являются
При этом точка
лежит на прямой а точка лежит на прямой Заданные прямые будут пересекаться, если выполнено условието есть векторы
компланарны (при этом их смешанное произведение равно нулю). ТогдаВычислим координаты точки пересечения прямых
и Для этого перепишем уравнения прямых в параметрической форме; получимПоскольку координаты
точки пересечения прямых должны удовлетворять обеим полученным системам уравнений, постольку приравнивая друг к другу соответствующие уравнения, получимСледовательно, заданные прямые пересекаются в точке с координатами
Об авторе:
Facta loquuntur.
Facta loquuntur.
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