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Консультация № 180258
10.10.2010, 12:55
0.00 руб.
0
5
1
помогите пожалуйста доказать тождество:
всё в векторах (a+2b-c)*(a-b)*(a-b-c)=-3*a*b*c
всё в векторах (a+2b-c)*(a-b)*(a-b-c)=-3*a*b*c
Обсуждение
10.10.2010, 13:15
общий
Посетитель - 339205:
Добрый день! Пусть a=b=c, (a+2b-c)*(a-b)*(a-b-c)=(a+2*a-a)*(a-a)*(a-a-a)=0
-3*a*b*c=-3*a*a*a. Тождество не выполняется, или я что-то не понимаю.
Добрый день! Пусть a=b=c, (a+2b-c)*(a-b)*(a-b-c)=(a+2*a-a)*(a-a)*(a-a-a)=0
-3*a*b*c=-3*a*a*a. Тождество не выполняется, или я что-то не понимаю.
10.10.2010, 13:35
общий
это ответ
Здравствуйте, Посетитель - 339205.
Речь, как я понимаю, про смешанное произведение векторов. Вспомним некоторые его свойства:
1) для него в силе дистрибутивный закон
2) от перемены мест двух множителей, знак меняется (антикоммутативность)
3) если все 3 вектора компланарны, векторное произведение равно нулю [$8658$] если из трёх векторов любые 2 равны (либо коллинеарны), векторное произведение равно нулю
Используем дистрибутивное свойство и раскрываем скобки (заведомо нулевые элементы сразу не пишу). Затем преобразуем, учитывая антикоммутативность.
Речь, как я понимаю, про смешанное произведение векторов. Вспомним некоторые его свойства:
1) для него в силе дистрибутивный закон
2) от перемены мест двух множителей, знак меняется (антикоммутативность)
3) если все 3 вектора компланарны, векторное произведение равно нулю [$8658$] если из трёх векторов любые 2 равны (либо коллинеарны), векторное произведение равно нулю
Используем дистрибутивное свойство и раскрываем скобки (заведомо нулевые элементы сразу не пишу). Затем преобразуем, учитывая антикоммутативность.
10.10.2010, 13:37
общий
lamed:
Если хотя бы 2 вектора коллинеарны, то смешанное произведение равно нулю
Если хотя бы 2 вектора коллинеарны, то смешанное произведение равно нулю
11.10.2010, 13:00
общий
Посетитель - 339205:
Обратите внимание, в условии задачи, предоставленной Вами должно получиться -3abc (со знаком минус),
а решение, предоставленное экспертом Roman Chaplinsky / Химик CH, показывает, что получается +3abc
Проверьте, пожалуйста, правильность записи исходного тождества.
Обратите внимание, в условии задачи, предоставленной Вами должно получиться -3abc (со знаком минус),
а решение, предоставленное экспертом Roman Chaplinsky / Химик CH, показывает, что получается +3abc
Проверьте, пожалуйста, правильность записи исходного тождества.
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
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