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Консультация № 196641
10.10.2019, 18:37
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Здравствуйте! Прошу помощи в следующем вопросе:Точки M и N-середины сторон BC и CD параллелограмма ABCD. Выразите вектор AC через векторы m=AM и n=AN. Заранее благодарен.
Обсуждение
12.10.2019, 21:26
общий
это ответ
Здравствуйте, Алексей Валентинович!
Рисунок, выполненный для наглядности изложенного ниже решения, находится в прикреплённом файле.
Имеем
Складывая уравнения (1), (2), получим
следовательно,
Если у Вас возникнут вопросы по предложенному решению задачи, то, пожалуйста, задавайте их в мини-форуме консультации.
Рисунок, выполненный для наглядности изложенного ниже решения, находится в прикреплённом файле.
Имеем
AM=AB+BM=AB+(1/2)BC; (1)
AN=AD+DN=BC+(1/2)DC=BC+(1/2)AB. (2)
Складывая уравнения (1), (2), получим
AM+AN=(AB+(1/2)BC)+(BC+(1/2)AB)=(3/2)(AB+BC)=(3/2)AC;
следовательно,
AC=(AM+AN)/(3/2)=(2/3)(AM+AN)=(2/3)(m+n)=(2/3)m+(2/3)n.
Если у Вас возникнут вопросы по предложенному решению задачи, то, пожалуйста, задавайте их в мини-форуме консультации.
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Об авторе:
Facta loquuntur.
Facta loquuntur.
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