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Даны три неколлениарных вектора а, b, и с. Найдите значения p и g, при которых векторы m=pa+gb+8c и h=а+pb+gc коллениарны

10-11 класс

Razym123 19 сент. 2014 г., 20:11:10 (9 лет назад)
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Dimbos95
19 сент. 2014 г., 21:34:02 (9 лет назад)

Запишем условие коллинеарности для векторов m и h:

m=Yh

pa+gb+8c =Y(а+pb+gc)

pa+gb+8c =Yа+Ypb+Ygc

pa=Ya, отсюда p=Y

gb=Ypb, отсюда g=Yp=p*p=p^2

8c=Ygc, отсюда 8=Yg=p*p^2=p^3, 8=p^3, p=2

g=p^2=2^2=4

 

Ответ:p=2, g=4

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