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Консультация № 199943
21.12.2020, 14:26
0.00 руб.
1
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Здравствуйте! У меня возникли сложности с таким вопросом:
"Вершины пирамиды находятся в точках А(5,3,6), B(-3,-4,4), C(5,-6,8), D(4,0,-3). Найти объем пирамиды и длину высоты, опущенной из вершины А."
Скрин прикладываю.
"Вершины пирамиды находятся в точках А(5,3,6), B(-3,-4,4), C(5,-6,8), D(4,0,-3). Найти объем пирамиды и длину высоты, опущенной из вершины А."
Скрин прикладываю.
Прикрепленные файлы:
Обсуждение
26.12.2020, 13:08
общий
это ответ
Здравствуйте, Alexander!
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
5
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