一.已知向量a=(-1,2),b=(4,3),m=b-入a,n=a+2b.(1)若入=-1/2,判断m与n是否平行,给出证明(2)若m垂直于n,求实数入的值.二.已知A为锐角,向量a=(cos(A-兀/6),sin(A-兀/6)),b=(根3,-1),且a?b=2/7.(1)若B为锐角,
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![一.已知向量a=(-1,2),b=(4,3),m=b-入a,n=a+2b.(1)若入=-1/2,判断m与n是否平行,给出证明(2)若m垂直于n,求实数入的值.二.已知A为锐角,向量a=(cos(A-兀/6),sin(A-兀/6)),b=(根3,-1),且a?b=2/7.(1)若B为锐角,](/uploads/image/z/10903004-44-4.jpg?t=%E4%B8%80.%E5%B7%B2%E7%9F%A5%E5%90%91%E9%87%8Fa%3D%EF%BC%88%EF%BC%8D1%2C2%EF%BC%89%2Cb%3D%284%2C3%29%2Cm%3Db-%E5%85%A5a%2Cn%3Da%2B2b.%281%29%E8%8B%A5%E5%85%A5%3D%EF%BC%8D1%EF%BC%8F2%2C%E5%88%A4%E6%96%ADm%E4%B8%8En%E6%98%AF%E5%90%A6%E5%B9%B3%E8%A1%8C%2C%E7%BB%99%E5%87%BA%E8%AF%81%E6%98%8E%EF%BC%882%EF%BC%89%E8%8B%A5m%E5%9E%82%E7%9B%B4%E4%BA%8En%2C%E6%B1%82%E5%AE%9E%E6%95%B0%E5%85%A5%E7%9A%84%E5%80%BC.%E4%BA%8C.%E5%B7%B2%E7%9F%A5A%E4%B8%BA%E9%94%90%E8%A7%92%2C%E5%90%91%E9%87%8Fa%3D%28cos%28A-%E5%85%80%2F6%29%2Csin%28A-%E5%85%80%2F6%29%29%2Cb%3D%28%E6%A0%B93%2C%EF%BC%8D1%29%2C%E4%B8%94a%3Fb%3D2%2F7.%281%29%E8%8B%A5B%E4%B8%BA%E9%94%90%E8%A7%92%2C)
一.已知向量a=(-1,2),b=(4,3),m=b-入a,n=a+2b.(1)若入=-1/2,判断m与n是否平行,给出证明(2)若m垂直于n,求实数入的值.二.已知A为锐角,向量a=(cos(A-兀/6),sin(A-兀/6)),b=(根3,-1),且a?b=2/7.(1)若B为锐角,
一.已知向量a=(-1,2),b=(4,3),m=b-入a,n=a+2b.(1)若入=-1/2,判断m与n是否平行,给出证明(2)若m垂直于n,求实数入的值.
二.已知A为锐角,向量a=(cos(A-兀/6),sin(A-兀/6)),b=(根3,-1),且a?b=2/7.(1)若B为锐角,且cos(A+B)=-11/14,求角B.(2)求sin2A-2根3cos方A/1+cos2A的值
一.已知向量a=(-1,2),b=(4,3),m=b-入a,n=a+2b.(1)若入=-1/2,判断m与n是否平行,给出证明(2)若m垂直于n,求实数入的值.二.已知A为锐角,向量a=(cos(A-兀/6),sin(A-兀/6)),b=(根3,-1),且a?b=2/7.(1)若B为锐角,
一,(1)——1/2看起来不爽,偶用0.5代替了
若入=-0.5,则m=(4-0.5×1,3+0.5×2)=(3.5,4)
n=(-1+2×4,2+2×3)=(7,8)
由m和n的坐标可以看出,n=2m
因此平行
(2)
m=(4+入,3-2入),n=(7,8)
因为垂直,所以m*n=28+7入+24-16入=0——偶用*代替向量算数量积的那个点
化得52-9入=0,入=52/9
二.(1)
a*b=根3×cos(A-兀/6)-sin(A-兀/6)=2/7
(根3/2)×cos(A-兀/6)-0.5×sin(A-兀/6)=1/7
cos兀/6×cos(A-兀/6)-sin兀/6×sin(A-兀/6)=1/7
cosA=1/7
sinA=4根3/7
cos(A+B)=cosAcosB-sinAsinB
=1/7×cosB-4根3/7×sinB=-11/14
与sin方B+cosB方=1连列,解方程……
此法不佳……很麻烦的……
解出来以后注意B的取值,取锐角
cosB=0.5
B=兀/3
(2)
原式=(2×sinA×cosA-2根3cos方A)/cos方A
=2×sinA/cosA-2根3
=2×tanA-2根3
=6根3