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Консультация № 199955
22.12.2020, 05:56
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Здравствуйте! Прошу помощи в следующем вопросе:
при каком значении p плоскости 2x+4y+6z-10=0 и -x-2y-pz+5=0 перпендекулярны
при каком значении p плоскости 2x+4y+6z-10=0 и -x-2y-pz+5=0 перпендекулярны
Обсуждение
12.07.2022, 06:41
общий
это ответ
Здравствуйте, spudymun1337!
Из курса аналитической геометрии известно, что две плоскости взаимно перпендикулярны тогда и только тогда, когда взаимно перпендикулярны их нормальные векторы. Если нормальные векторы перпендикулярны, то их скалярное произведение равно нулю.
В рассматриваемом случае нормальные векторы суть
и 
Приравняв к нулю их скалярное произведение, получим, что
Из курса аналитической геометрии известно, что две плоскости взаимно перпендикулярны тогда и только тогда, когда взаимно перпендикулярны их нормальные векторы. Если нормальные векторы перпендикулярны, то их скалярное произведение равно нулю.
В рассматриваемом случае нормальные векторы суть
и Приравняв к нулю их скалярное произведение, получим, что
Об авторе:
Facta loquuntur.
Facta loquuntur.
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