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Консультация № 164379
07.04.2009, 20:38
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Единичные вектора а и с образовывают угол 120 градусов. Вычислите сумму квадратов длин всех сторон параллелограмма, постороенного на векторах 2а-с и а+2с.
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Обсуждение
Неизвестный
08.04.2009, 08:49
общий
это ответ
Здравствуйте, Kafka!
Дано: |a| = |c| = 1;
<a,c> = cos(120) = -0,5; <a,c>- скалярное произведение.
Найти: 2|2a-c|^2 + 2|a+2c|^2.
Решение:
|2a-c|^2 = <(2a-c),(2a-c)> = <2a,2a> - 2<2a,c> + <c,c> = 4 - 4cos(120) + 1 = 7,
|a+2c|^2 = <(a+2c),(a+2c)> = <a,a> + 2<a,2c> + <2c,2c> = 1 + 4cos(120) + 4 = 3.
Ответ: сумма квадратов длин всех сторон параллелограмма равна 2(7 + 3) = 20
Дано: |a| = |c| = 1;
<a,c> = cos(120) = -0,5; <a,c>- скалярное произведение.
Найти: 2|2a-c|^2 + 2|a+2c|^2.
Решение:
|2a-c|^2 = <(2a-c),(2a-c)> = <2a,2a> - 2<2a,c> + <c,c> = 4 - 4cos(120) + 1 = 7,
|a+2c|^2 = <(a+2c),(a+2c)> = <a,a> + 2<a,2c> + <2c,2c> = 1 + 4cos(120) + 4 = 3.
Ответ: сумма квадратов длин всех сторон параллелограмма равна 2(7 + 3) = 20
Форма ответа
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