数学急!在ABC中,ABC对应a,b,c,向量m=(b,a-2c),向量n=(cosA-2cosC,cosB),且m垂直n(1)求sinC/sinA的值()若a=2,向量m的模=3根号5,求ABC面积
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![数学急!在ABC中,ABC对应a,b,c,向量m=(b,a-2c),向量n=(cosA-2cosC,cosB),且m垂直n(1)求sinC/sinA的值()若a=2,向量m的模=3根号5,求ABC面积](/uploads/image/z/5547691-19-1.jpg?t=%E6%95%B0%E5%AD%A6%E6%80%A5%21%E5%9C%A8ABC%E4%B8%AD%2CABC%E5%AF%B9%E5%BA%94a%2Cb%2Cc%2C%E5%90%91%E9%87%8Fm%3D%28b%2Ca-2c%29%2C%E5%90%91%E9%87%8Fn%3D%28cosA-2cosC%2CcosB%29%2C%E4%B8%94m%E5%9E%82%E7%9B%B4n%EF%BC%881%EF%BC%89%E6%B1%82sinC%2FsinA%E7%9A%84%E5%80%BC%EF%BC%88%EF%BC%89%E8%8B%A5a%3D2%2C%E5%90%91%E9%87%8Fm%E7%9A%84%E6%A8%A1%3D3%E6%A0%B9%E5%8F%B75%2C%E6%B1%82ABC%E9%9D%A2%E7%A7%AF)
数学急!在ABC中,ABC对应a,b,c,向量m=(b,a-2c),向量n=(cosA-2cosC,cosB),且m垂直n(1)求sinC/sinA的值()若a=2,向量m的模=3根号5,求ABC面积
数学急!在ABC中,ABC对应a,b,c,向量m=(b,a-2c),
向量n=(cosA-2cosC,cosB),且m垂直n(1)求sinC/sinA的值()若a=2,向量m的模=3根号5,求ABC面积
数学急!在ABC中,ABC对应a,b,c,向量m=(b,a-2c),向量n=(cosA-2cosC,cosB),且m垂直n(1)求sinC/sinA的值()若a=2,向量m的模=3根号5,求ABC面积
(1)
m⊥n
m.n=0
(b,a-2c).(cosA-2cosC,cosB)=0
b(cosA-2cosC)+(a-2c)cosB=0
b[(b^2+c^2-a^2)/(2bc)- 2(a^2+b^2-c^2)/(2ab)] +(a-2c)[(a^2+c^2-b^2)/(2ac)]=0
b[a(b^2+c^2-a^2)-2c(a^2+b^2-c^2)] +b(a-2c)(a^2+c^2-b^2) =0
ab(2c^2)-2bc(2a^2)=0
c-2a=0
c=2a
by sine rule
a/sinA = c/sinC
sinA/sinC = a/c = a/(2a) = 1/2
(2)
a=2
=> c= 4
|m|=3√5
=> b^2+(a-2c)^2=45
b^2+a^2+4c^2-4ac =45
b^2 +4+ 64-32=45
b= 3
cosA = (b^2+c^2-a^2)/(2bc)
= (9+16-4)/(24)
= 7/8
sinA = √15/8
Area
=(1/2)bcsinA
=(1/2)(3)(4) √15/8
=3√15/4