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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос: Даны 3 вершины треугольника. Вычислить а) квадрат длины вектора (D_1 D_2 ) ̅ достроив треугольник до параллелограммов ABCD_1 и ABD_2 C б) координаты точки пересечения диагоналей параллелограмма ABCD_1 в) координаты точки пересечения медиан треугольника ABC г) координаты вектора с началом в точке C равного вектору (BA) ̅ д) работу силы (AD) ̅ на пути ABCD. A(1;1; -2),B(2;3; -3),C(-1; -2;1)
Смысл задания пункта г) мне тоже непонятен. А чтобы выполнить задание пункта д), Вам нужно исходить из определения работы постоянной силы на прямолинейном участке пути. Сообщите это определение.
б) Диагонали параллелограмма делятся точкой пересечения пополам. Поэтому если -- точка пересечения диагоналей параллелограмма то точка делит отрезок пополам и
-- точка пересечения диагоналей параллелограмма
в)
Медианы треугольника пересекаются в одной точке и делятся в отношении считая от вершин, из которых они проведены. Отрезок -- медиана треугольника, проведённая из вершины Если -- точка пересечения медиан этого треугольника, то
-- точка пересечения медиан треугольника
г)
Насколько я понимаю, любой вектор, равный вектору независимо от точки приложения его начала, включая точку имеет те же координаты, что и вектор Однако, формулировка задания пункта г): Цитата: Кириллова Анна Витальевна
Найти ... г) координаты вектора с началом в точке C равного вектору (BA) ?
настолько витиеватая, что я могу предположить, что автор Вашего задания имел в виду координаты вектора, равного сумме векторов и Тогда
д)
Работа силы на пути равна работе силы на пути и равна сумме скалярных произведений вектора на векторы
Я не уверен, что в моём решении нет ошибок. Поэтому, пожалуйста, сравните результаты своих расчётов с моими и, если будут расхождения, то, пожалуйста, сообщите. При необходимости я внесу изменения в свой ответ. Срок действия консультации я продлил.
Здравствуйте! Извиняюсь, что долго не отвечала. У меня все сошлось кроме последнего задания: D(-2; -4; 2) CD=(-2; -4; 2)-(-1; -2;1)=(-1; -2;1) AD=(-2; -4; 2)-(1;1; -2)=(-3; -5;4) Рассмотрим пути AB,BC,CD. Работа силы на пути равна скалярному произведению векторов AD*AB+AD*BC+AD*CD=(-3; -5;4)*(1;2;-1)+(-3; -5;4)*(-3;-5;4)+(-3; -5;4)*(-1; -2;1)=(-3*1+(-5)*2+4*(-1))+(-3*(-3)+(-5)*(-5)+4*4)+(-3*(-1)+(-5)*(-2)+4*1)=50
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involve 
Они Вам известны?
на участке 
? Вычислите, пожалуйста, и сообщите.
-- вершина параллелограмма.
-- вершина параллелограмма.
-- точка пересечения диагоналей параллелограмма 
то точка 
пополам и
-- точка пересечения диагоналей параллелограмма 
считая от вершин, из которых они проведены. Отрезок 
-- медиана треугольника, проведённая из вершины 
Если 
-- точка пересечения медиан этого треугольника, то
-- точка пересечения медиан треугольника 
независимо от точки приложения его начала, включая точку 
имеет те же координаты, что и вектор 
и 
равна работе силы 
на пути 
