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Консультация № 200247
09.02.2021, 16:53
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
Вершины пирамиды находятся в точках А(7,4,9), В(1,−2,−3), С(−5,−3,0), D(1,−3,4). Найти
объем пирамиды и длину высоты, опущенной из вершины С.
Вершины пирамиды находятся в точках А(7,4,9), В(1,−2,−3), С(−5,−3,0), D(1,−3,4). Найти
объем пирамиды и длину высоты, опущенной из вершины С.
Прикрепленные файлы:
Обсуждение
14.02.2021, 07:12
общий
это ответ
Здравствуйте, ALX5!
Пусть имеются три вектора a, b, c с общим началом и не лежащие в одной плоскости (некомпланарные). Тогда объём параллелепипеда, построенного на этих векторах, будет равен модулю их смешанного произведения, объём же пирамиды будет в шесть раз меньше:
Для параллелепипеда площадь основания - параллелограмма, построенного на векторах b и c, равна модулю их векторного произведения, для пирамиды площадь лежащего в основании треугольника будет вдвое меньше:
Поскольку для пирамиды V = SH/3, её высота будет равна
В данном случае в качестве векторов a, b, c можно взять соответственно вектора
Тогда соответствующие смешанное и векторное произведения определяются по формулам векторной алгебры как
а искомые объём и высота пирамиды будут равны
Пусть имеются три вектора a, b, c с общим началом и не лежащие в одной плоскости (некомпланарные). Тогда объём параллелепипеда, построенного на этих векторах, будет равен модулю их смешанного произведения, объём же пирамиды будет в шесть раз меньше:
Для параллелепипеда площадь основания - параллелограмма, построенного на векторах b и c, равна модулю их векторного произведения, для пирамиды площадь лежащего в основании треугольника будет вдвое меньше:
Поскольку для пирамиды V = SH/3, её высота будет равна
В данном случае в качестве векторов a, b, c можно взять соответственно вектора
Тогда соответствующие смешанное и векторное произведения определяются по формулам векторной алгебры как
а искомые объём и высота пирамиды будут равны
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