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Консультация № 159858
07.02.2009, 15:11
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1
Вектора а и с образуют угол 60 градусов и |a|=9, |c|=2. Найдите |а+с| ;
Заранее огромное спасибо!
Заранее огромное спасибо!
Обсуждение
08.02.2009, 04:22
общий
это ответ
Здравствуйте, Kafka!
Проведем вектор a+c, соединяющий начало вектора а и конец вектора, начинающегося с конца вектора а
и параллельного исходному вектору с
Так как угол между вектором а и с равен 60 градусов, то тупой угол в получившемся треугольнике будет равен 120 градусов.
По теореме косинусов имеем (|a+c|)2 = |a|2 + |c|2 - 2|a||c| cos(120) = 92 + 22 + 2*9*2*cos(60) =
81 + 4 + 18 = 103. Т.о. |a+c| = sqrt(103)
Проведем вектор a+c, соединяющий начало вектора а и конец вектора, начинающегося с конца вектора а
и параллельного исходному вектору с
Так как угол между вектором а и с равен 60 градусов, то тупой угол в получившемся треугольнике будет равен 120 градусов.
По теореме косинусов имеем (|a+c|)2 = |a|2 + |c|2 - 2|a||c| cos(120) = 92 + 22 + 2*9*2*cos(60) =
81 + 4 + 18 = 103. Т.о. |a+c| = sqrt(103)
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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