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Консультация № 117736
10.01.2008, 09:44
0.00 руб.
0
2
1
При каком значении "Лямбда" векторы а=( "Лямбда";3;0) и b=( "Лямбда";-12;1) j,образуют тупой угол?
Обсуждение
Неизвестный
10.01.2008, 14:38
общий
это ответ
Здравствуйте, Савкина Ирина Валерьевна!
Т.к косинус тупого угла отрицательный, то необходимо решить неравенство:
cos(a,b)<0
(lambda,3,0)·(lambda,-12,1)/(sqrt(lambda²+3²)·sqrt(lambda²+12²)))<0
(lambda²-36)/(sqrt(lambda²+9)·sqrt(lambda²+124)))<0
Т.к. знаменатель положительный не зависимо от лямбда, то данное неравенство равносильно неравенству:
lambda²-36<0
lambda²<36
-6<lambda<6
Значит, при lambda из промежутка (-6;6) вектора a и b образуют тупой угол.
Т.к косинус тупого угла отрицательный, то необходимо решить неравенство:
cos(a,b)<0
(lambda,3,0)·(lambda,-12,1)/(sqrt(lambda²+3²)·sqrt(lambda²+12²)))<0
(lambda²-36)/(sqrt(lambda²+9)·sqrt(lambda²+124)))<0
Т.к. знаменатель положительный не зависимо от лямбда, то данное неравенство равносильно неравенству:
lambda²-36<0
lambda²<36
-6<lambda<6
Значит, при lambda из промежутка (-6;6) вектора a и b образуют тупой угол.
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