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Консультация № 194168
13.12.2018, 20:44
0.00 руб.
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1
Здравствуйте! Прошу помощи в следующем вопросе:
Записать матрицу перехода от ортонормированного базиса e1 =(1,0,0);
e2 =(0,1,0); e3 =(0,0,1) к базису e1', e2' , e3' , если он образован путем
поворота первого базиса вокруг вектора ei на угол α.
Вектор
ei=e2; Угол
α=-П/3
Записать матрицу перехода от ортонормированного базиса e1 =(1,0,0);
e2 =(0,1,0); e3 =(0,0,1) к базису e1', e2' , e3' , если он образован путем
поворота первого базиса вокруг вектора ei на угол α.
Вектор
ei=e2; Угол
α=-П/3
Обсуждение
14.12.2018, 10:06
общий
14.12.2018, 10:19
Адресаты:
protasyuk.vladimir Записать матрицу перехода
Сообщите, пожалуйста, что значит "записать матрицу". Нужен вывод этой матрицы или нет? Достаточно ли в матрицу поворота вокруг оси ординат подставить значения синуса и косинуса для заданного угла поворота?
Об авторе:
Facta loquuntur.
Facta loquuntur.
16.12.2018, 21:15
общий
это ответ
Здравствуйте, protasyuk.vladimir!
В результате поворота первого базиса относительно вектора
на угол 
имеем
Поэтому матрица
перехода от базиса 
к базису 
имеет вид
(она получается, если привести координаты векторов нового базиса в столбцах).
Если
то 
Литература. Аналитическая геометрия в примерах и задачах: Учеб. пособие / А. С. Бортаковский, А. В. Пантелеев. -- М.: Высш. шк., 2005. -- 496 с.
В результате поворота первого базиса относительно вектора
на угол имеемПоэтому матрица
перехода от базиса к базису имеет вид(она получается, если привести координаты векторов нового базиса в столбцах).
Если
то Литература. Аналитическая геометрия в примерах и задачах: Учеб. пособие / А. С. Бортаковский, А. В. Пантелеев. -- М.: Высш. шк., 2005. -- 496 с.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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