名校
1 . 如图,两条异面直线a,b所成角为
,在直线a,b上分别取点
,E和点A,F,使
且
.已知
,
,
.则线段
的长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b8df14d11c6f036b3b248544b731ae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd72669c08e98a92cdfb9bc167ac56bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/078094de8f667321aa782b0f62242afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae341f580ff8fbf21f616fe900b0e4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7454ed55c9f309bac5e60df058e596.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/1f48148b-24ca-4c59-8417-65b4ecbed67b.png?resizew=141)
A.2或![]() | B.4 |
C.2或4 | D.4或![]() |
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解题方法
2 . 已知直线
,且
,
(1)求
的值;
(2)直线
过点
与
交于
,
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06626397bccdcb7e16acc3780a68ed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e03566282ef39ad17821036f228174.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd3287fe7ab879d8756115a5d4d22d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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3 . 如图,棱长为1的正四面体OABC中,
,点M满足
,点N为BC中点,
(1)用
表示
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352afb2166bc2d282d55bd7bba4388e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6aa2a7c840613899fac45f7dd04789.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/1c7eeec9-53b3-460d-9f40-66d6f6d81a6f.png?resizew=148)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3352ef5f607b600467e786b4e0654e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4ea7acf140086ae816a4025d2683dc.png)
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4 . 已知向量
.
(1)若
,求实数
;
(2)若向量
与
所成角为钝角,求实数
的范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d14bffb4c83a054c9d0dcc1f85b7d9c2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a75525d27a7793d7cf698e16a7d809.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49bc70bb27f9dc49c97fe6b5ccd018d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed492f7b29166ba5c1f0023b05a439c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
5 . 已知点
,直线
过点
,
(1)若A到直线
距离为2,求直线
的方程;
(2)若A、B到直线
距离相等,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3019637dd642f6ef50444b2efcfec03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
(1)若A到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若A、B到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
6 . 棱长为
的正方体
中,
分别是平面
和平面
内动点,
,则
的最小值为_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6229543ce04b1465a341672391974661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ddeb7ce17137144641f061042c14fb.png)
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2023-11-09更新
|
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重庆市开州中学2023-2024学年高二上学期第一次月考数学试题广东省深圳市深圳实验学校高中园2023-2024学年高二上学期期末考试数学试题(已下线)压轴小题5 空间向量中的最值问题(已下线)广东省深圳市深圳外国语学校2024届高三上学期第二次模拟测试数学试题变式题11-16
7 . 已知
,则
在
上的投影向量为_______ (用坐标表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9483cf97e95c3d47c3cf22595757ae4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
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解题方法
8 . 直线
过点
,且斜率是倾斜角为
的直线斜率的二倍,则直线
的方程为_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
9 . 已知点
,
,直线
上存在点P满足
,则直线
可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfaba0309c471a4246ca3254a3cdaf17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baca988e757625c577e02752422a72d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c411141bb6f671d152b82f5e39e10a04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010c7e4c1ad92debbd311dfd81229dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.-2 | B.0 | C.1 | D.3 |
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10 . 如图,在棱长为1的正方体
中,
为线段
的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/6bb8639d-1ba3-47fb-b6c2-b88e5d159e29.png?resizew=161)
A.四面体![]() ![]() |
B.向量![]() ![]() ![]() |
C.直线![]() ![]() |
D.直线![]() ![]() ![]() |
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2023-11-09更新
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