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Консультация № 202119
31.01.2022, 11:09
0.00 руб.
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1
Здравствуйте, уважаемые эксперты! Прошу подсказки в решении (задание прикрепила). Уже пыталась решить с условием что у коллинеарных векторов координаты пропорциональны,а у перпендикулярных-скалярное произведение равно 0.,к сожалению не получилось
Прикрепленные файлы:
Обсуждение
31.01.2022, 13:39
общий
Адресаты:
Даны 2 вектора : a[$8594$] = {2; -1; 3} , b[$8594$] = {-2; -1; -2} .
Найти векторы x[$8594$] , y[$8594$] , удовлетворяющие условиям : x[$8594$] [$8214$] a[$8594$] , y[$8594$] [$8869$] b[$8594$] , x[$8594$] + y[$8594$] = b[$8594$]
Решение: Кто забыл, как работать с векторами, читаем учебную статью "Векторы для чайников. Действия с векторами. Координаты вектора. Простейшие задачи с векторами" Ссылка1
Предлагаю Вам Решение в популярном приложении Маткад (ссылка2) . Маткад избавляет меня от ошибок. Маткад-скриншот прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Ответ: x[$8594$] = {-2; 1; -3} , y[$8594$] = {0; -2; 1} , Проверка сделана.
Пояснения : Ключевое слово solve,k означает Решить уравнение, прописанное слева от solve относительно искомой переменной k .
Символ := означает оператор присваивания. Символ [$8594$] - вывести на экран в символьном виде (имена переменных с операндами либо в виде простой, неокруглённой дроби).
Оператор stack(A, B, C, …) объединяет числовые данные в вектор-столбец.
Найти векторы x[$8594$] , y[$8594$] , удовлетворяющие условиям : x[$8594$] [$8214$] a[$8594$] , y[$8594$] [$8869$] b[$8594$] , x[$8594$] + y[$8594$] = b[$8594$]
Решение: Кто забыл, как работать с векторами, читаем учебную статью "Векторы для чайников. Действия с векторами. Координаты вектора. Простейшие задачи с векторами" Ссылка1
Предлагаю Вам Решение в популярном приложении Маткад (ссылка2) . Маткад избавляет меня от ошибок. Маткад-скриншот прилагаю . Я добавил в скрин подробные комментарии зелёным цветом.
Пояснения : Ключевое слово solve,k означает Решить уравнение, прописанное слева от solve относительно искомой переменной k .
Символ := означает оператор присваивания. Символ [$8594$] - вывести на экран в символьном виде (имена переменных с операндами либо в виде простой, неокруглённой дроби).
Оператор stack(A, B, C, …) объединяет числовые данные в вектор-столбец.
31.01.2022, 18:05
общий
это ответ
Здравствуйте, Виктория!
Пусть
Требуется определить векторы 
и 
такие, что вектор параллелен вектору 
вектор перпендикулярен вектору 
Поскольку вектор параллелен вектору постольку 
где 
-- вещественное число, которое по смыслу задачи нужно вычислить.
Поскольку вектор
перпендикулярен вектору постольку скалярное произведение этих векторов равно нулю, то есть 
Поскольку
постольку 
то есть 
Значит,
-- искомый вектор
-- искомый вектор
Пусть
Требуется определить векторы и такие, что вектор параллелен вектору вектор перпендикулярен вектору Поскольку вектор
параллелен вектору постольку где -- вещественное число, которое по смыслу задачи нужно вычислить.Поскольку вектор
перпендикулярен вектору постольку скалярное произведение этих векторов равно нулю, то есть Поскольку
постольку то есть Значит,
-- искомый вектор
-- искомый вектор
Об авторе:
Facta loquuntur.
Facta loquuntur.
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