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Консультация № 173811
29.10.2009, 10:00
25.00 руб.
0
3
1
Добрый день! Помогите решить задачку: прирамида abcd, ad =24, bc=10, растояние между серединами bd и ас 13, найти угом между прямыми ad и вс.
Обсуждение
29.10.2009, 11:25
общий
это ответ
Здравствуйте, Словик.В.А.
Задача хорошо решается с помощью векторной алгебры.
По условию AD = 24, BС = 10, PQ = 13.
Запишем два векторных уравнения:
AD = CB + BD - CA
PQ = CB + BD/2 - CA/2.
Умножим второе уравнение на 2 и вычтем из первого. Получим:
AD - 2*PQ = -CB, или
AD + CB = 2*PQ.
Возведем обе части в квадрат:
AD2 + 2*AD*CB + CB2 = 4*PQ2.
Учитывая, что AD*CB = AD*CB*cos[$945$], найдем
cos[$945$] = (4*PQ2 - AD2 - CB2)/(2*AD*CB).
Подставляя численные значения, находим cos[$945$] = 0, то есть, прямые AD и BC перпендикулярны.
Задача хорошо решается с помощью векторной алгебры.
По условию AD = 24, BС = 10, PQ = 13.
Запишем два векторных уравнения:
AD = CB + BD - CA
PQ = CB + BD/2 - CA/2.
Умножим второе уравнение на 2 и вычтем из первого. Получим:
AD - 2*PQ = -CB, или
AD + CB = 2*PQ.
Возведем обе части в квадрат:
AD2 + 2*AD*CB + CB2 = 4*PQ2.
Учитывая, что AD*CB = AD*CB*cos[$945$], найдем
cos[$945$] = (4*PQ2 - AD2 - CB2)/(2*AD*CB).
Подставляя численные значения, находим cos[$945$] = 0, то есть, прямые AD и BC перпендикулярны.
Форма ответа
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