两条直线L1:(m+3)x+2y=5-3m,L2:4x+(5+m)y=16,则m为何值时,l1到l2的角为45度l1与l2的夹角为45度这两个问题有什么不同的么= =
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![两条直线L1:(m+3)x+2y=5-3m,L2:4x+(5+m)y=16,则m为何值时,l1到l2的角为45度l1与l2的夹角为45度这两个问题有什么不同的么= =](/uploads/image/z/3243633-33-3.jpg?t=%E4%B8%A4%E6%9D%A1%E7%9B%B4%E7%BA%BFL1%3A%28m%2B3%29x%2B2y%3D5-3m%2CL2%3A4x%2B%285%2Bm%29y%3D16%2C%E5%88%99m%E4%B8%BA%E4%BD%95%E5%80%BC%E6%97%B6%2Cl1%E5%88%B0l2%E7%9A%84%E8%A7%92%E4%B8%BA45%E5%BA%A6l1%E4%B8%8El2%E7%9A%84%E5%A4%B9%E8%A7%92%E4%B8%BA45%E5%BA%A6%E8%BF%99%E4%B8%A4%E4%B8%AA%E9%97%AE%E9%A2%98%E6%9C%89%E4%BB%80%E4%B9%88%E4%B8%8D%E5%90%8C%E7%9A%84%E4%B9%88%3D+%3D)
两条直线L1:(m+3)x+2y=5-3m,L2:4x+(5+m)y=16,则m为何值时,l1到l2的角为45度l1与l2的夹角为45度这两个问题有什么不同的么= =
两条直线L1:(m+3)x+2y=5-3m,L2:4x+(5+m)y=16,则m为何值时,
l1到l2的角为45度
l1与l2的夹角为45度
这两个问题有什么不同的么= =
两条直线L1:(m+3)x+2y=5-3m,L2:4x+(5+m)y=16,则m为何值时,l1到l2的角为45度l1与l2的夹角为45度这两个问题有什么不同的么= =
L1:(m+3)x+2y=5-3m,那么斜率k1=-(m+3)/2
L2:4x+(5+m)y=16,那么斜率k2=-4/(5+m)
l1到l2 的角是45度,则有tan45=(k2-k1)/(1+k1k2)=(-4/(5+m)+(m+3)/2)/(1+4/(5+m)*(m+3)/2)=1
即有:-8+(m+3)(m+5)=2(5+m)+4(m+3)
-8+m^2+8m+15=10+2m+4m+12
m^2+2m-15=0
(m+5)(m-3)=0
m+5不=0,则有m=3
当m+5=0 时,l2:x=4,L1:-2x+2y=20,即有y=x+10,二直线成45度的角,符合
即有m=-5或m=3
(2)L1与L2的夹角是45度,则有tan45=|(k1-k2)/(1+k1k2)|
即有|(-4/(5+m)+(m+3)/2)/(1+4/(5+m)*(m+3)/2)|=1
即有|-8+(m+3)(m+5)|=|2(5+m)+4(m+3)|
|m^2+8m+7|=|6m+22|
m^2+8m+7=6m+22,或m^2+8m+7=-6m-22
(m+5)*(m-3)=0 或m^2+14m+29=0
即有m=-5或3, (m+7)^2=20
m=-7土2根号5
即有m=-5或3或-7土2根号5