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Консультация № 159365
01.02.2009, 21:48
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Помогите пожалуйста решить задачу! Даны диагонали параллелограмма d1= i - 2j + 3k; d2 {-1;2;-1}. Найти его площадь и длину одной из высот!
Обсуждение
Неизвестный
02.02.2009, 16:15
общий
это ответ
Здравствуйте, Appolo!
1) Найдем длину d1 и d2: |d1|=sqrt(1+4+9)=sqrt(14), |d2|=sqrt(1+4+1)=sqrt(6)
S=1/2*d1*d2*sin(fi)
cos(fi)=a*b/|a|*|b|=(1*(-1)-2*2+3*(-1))/2sqrt(21)=-4/sqrt(21)
sin(fi)=sqrt(1-(cos(fi)^2)) => sin(fi)=sqrt(5/21)
Итак, S=1/2*sqrt(14*6)*sqrt(5/21)=sqrt(5)
2) h_a=S/a. Найдем а: a^2=(d1/2)^2+(d2/2)^2-2*d1/2*d2/2*cos(alfa) =>
a^2=14/4+6/4-1/2*sqrt(21)*(-4/sqrt(21))=5+4=9 => a=3
h_A=sqrt(5)/3.
1) Найдем длину d1 и d2: |d1|=sqrt(1+4+9)=sqrt(14), |d2|=sqrt(1+4+1)=sqrt(6)
S=1/2*d1*d2*sin(fi)
cos(fi)=a*b/|a|*|b|=(1*(-1)-2*2+3*(-1))/2sqrt(21)=-4/sqrt(21)
sin(fi)=sqrt(1-(cos(fi)^2)) => sin(fi)=sqrt(5/21)
Итак, S=1/2*sqrt(14*6)*sqrt(5/21)=sqrt(5)
2) h_a=S/a. Найдем а: a^2=(d1/2)^2+(d2/2)^2-2*d1/2*d2/2*cos(alfa) =>
a^2=14/4+6/4-1/2*sqrt(21)*(-4/sqrt(21))=5+4=9 => a=3
h_A=sqrt(5)/3.
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