10.
已知命题:“平面内
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao88/42b9abf6aabc452b0dfac2f8b619a519.png)
与
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao74/357f54e25abf1c2253c349f620d1145e.png)
是一组不平行向量,且|
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao88/42b9abf6aabc452b0dfac2f8b619a519.png)
|=|
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao74/357f54e25abf1c2253c349f620d1145e.png)
|=1,
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao22/59cec0dafd99e3f787f5c5828735e11c.png)
,则任一非零向量
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao96/27547458eadcb16ee8c9ab2e2da3d90b.png)
,
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao96/27547458eadcb16ee8c9ab2e2da3d90b.png)
=λ
1![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao88/42b9abf6aabc452b0dfac2f8b619a519.png)
+λ
2![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao74/357f54e25abf1c2253c349f620d1145e.png)
(λ
1,λ
2∈R),若点P在过点O(不与OA重合)的直线l上,则
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao4/9fd33505d4f318e3ec04387206153472.png)
=k(定值),反之也成立,我们称直线l为以
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao88/42b9abf6aabc452b0dfac2f8b619a519.png)
与
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao74/357f54e25abf1c2253c349f620d1145e.png)
为基底的等商线,其中定值k为直线l的等商比.”为真命题,则下列结论中成立的是
______
(填上所有真命题的序号).
①当k=1时,直线l经过线段AB中点;
②当k<-1时,直线l与AB的延长线相交;
③当k=-1时,直线l与AB平行;
④l
1⊥l
2时,对应的等商比满足k
1•k
2=-1;
⑤直线l
1与l
2的夹角记为θ(θ≠
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao13/3cfe99ea77d11541d9753038d56a5aa4.png)
)对应的等商比为k
1、k
2,则tanθ=
![](https://www.ebk.net.cn/tikuimages/2/2016/700/shoutiniao61/5977b84ff0ac187cff2b3eb4b14de6fe.png)
.