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Консультация № 195074
27.03.2019, 17:25
0.00 руб.
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5
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Здравствуйте! У меня возникли сложности с таким вопросом:
В параллелепипеде ABCDA1B1C1D1 точки M и N - центры граней A1B1C1D1 и BB1C1C. Постройте сечение параллелепипеда плоскостью ANM и определите, в каком отношении эта плоскость делит диагональ DB1.
В параллелепипеде ABCDA1B1C1D1 точки M и N - центры граней A1B1C1D1 и BB1C1C. Постройте сечение параллелепипеда плоскостью ANM и определите, в каком отношении эта плоскость делит диагональ DB1.
Обсуждение
29.03.2019, 10:31
общий
Адресаты:
Требуемое сечение я построил быстро, а с вычислением отношения возникли проблемы. Откуда Вы взяли эту задачу?
Об авторе:
Facta loquuntur.
Facta loquuntur.
29.03.2019, 19:55
общий
Адресаты:
Alik В гимназии дали как дополнительную задачу, кто хочет может порешать
Похвально, что Вы взялись порешать эту задачу. Сообщите, пожалуйста, что у Вас получилось.
Результаты моей работы следующие:
1) построенное сечение ARQS показано в прикреплённом файле;
2) |B1U|:|UD|=2:3.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
30.03.2019, 07:14
общий
это ответ
Здравствуйте, Alik!
Построенное сечение ARQS показано в прикреплённом файле. Построение было выполнено в такой последовательности. Сначала была определена точка P как результат пересечения прямых AM и CC1. Проведя прямую PN, определили положение точек Q и S как результатов пересечения этой прямой с прямыми B1C1 и BC соответственно. Проведя прямую QM, определили положение точки R как результата пересечения с прямой A1D1. Получили сечение параллелепипеда плоскостью ANM. Это сечение ARQS -- параллелограмм: в нём [AS]//[QR], [AR]//[QS] как отрезки прямых, являющихся результатами пересечения плоскости ANM с попарно параллельными гранями параллелепипеда.
Далее определили положение точки T как результата пересечения прямой BD с прямой AS. Соединив точку T с точкой M, определили положение точки U, в которой диагональ [DB1] пересекается с плоскостью ANM.
Далее, рассматривая плоскости ABC и A1B1C1, установили, что |A1R}=|QS1|=|BS|, |C1Q|:|CS|=|PC1|:|PC|=1:2, откуда |C1Q|=|BS|=1/2*|CS|. Тогда |BT|:|TD|=1:3, |BT|=1/4*|BD|, и, поскольку |B1M|=1/2*|BD|, постольку |B1U|:|UD|=|B1M|:|TD|=2:3.
Построенное сечение ARQS показано в прикреплённом файле. Построение было выполнено в такой последовательности. Сначала была определена точка P как результат пересечения прямых AM и CC1. Проведя прямую PN, определили положение точек Q и S как результатов пересечения этой прямой с прямыми B1C1 и BC соответственно. Проведя прямую QM, определили положение точки R как результата пересечения с прямой A1D1. Получили сечение параллелепипеда плоскостью ANM. Это сечение ARQS -- параллелограмм: в нём [AS]//[QR], [AR]//[QS] как отрезки прямых, являющихся результатами пересечения плоскости ANM с попарно параллельными гранями параллелепипеда.
Далее определили положение точки T как результата пересечения прямой BD с прямой AS. Соединив точку T с точкой M, определили положение точки U, в которой диагональ [DB1] пересекается с плоскостью ANM.
Далее, рассматривая плоскости ABC и A1B1C1, установили, что |A1R}=|QS1|=|BS|, |C1Q|:|CS|=|PC1|:|PC|=1:2, откуда |C1Q|=|BS|=1/2*|CS|. Тогда |BT|:|TD|=1:3, |BT|=1/4*|BD|, и, поскольку |B1M|=1/2*|BD|, постольку |B1U|:|UD|=|B1M|:|TD|=2:3.
Прикрепленные файлы:
Об авторе:
Facta loquuntur.
Facta loquuntur.
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