名校
1 . 已知正方体
的棱长为1,以
为原点,
为单位正交基底,建立空间直角坐标系,则平面
的一个法向量是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5707c9498f4d24980badeb73e9afe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a211ad5a06b505b8365a62c1946f3cb7.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-03-15更新
|
149次组卷
|
7卷引用:北京市丰台区第二中学2022-2023学年高二上学期10月月考数学试卷
北京市丰台区第二中学2022-2023学年高二上学期10月月考数学试卷湖北省荆州市沙市中学2022-2023学年高二上学期期末数学试题(已下线)2.4.1 空间直线的方向向量和平面法向量(同步练习)-【素养提升—课时练】2022-2023学年高二数学湘教版选择性必修第二册检测(提高篇)(已下线)1.4.1 用空间向量研究直线、平面的位置关系(第2课时)(导学案) -【上好课】高二数学同步备课系列(人教A版2019选择性必修第一册)(已下线)第05讲 1.4.1 用空间向量研究直线、平面的位置关系(1)(已下线)期末测试卷02(测试范围:第1-4章数列)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)(已下线)第七章 立体几何与空间向量 第五节 空间向量与线、面位置关系 讲
名校
解题方法
2 . 在平面直角坐标系中,直线
经过
两点,
经过
两点,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ ;若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ccf06906b9ecdff9b539608ebc781d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/605c4c8d3bb9cb6d27df32ed51f252f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02e03566282ef39ad17821036f228174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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3 . 已知空间向量
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338189ec20d1ec7fdbbc189d209428dd.png)
______ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c25d90876e69e7156237e9ebf7e4c17.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63f8d142a854c5de3e4731c28f33f864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338189ec20d1ec7fdbbc189d209428dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c25d90876e69e7156237e9ebf7e4c17.png)
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解题方法
4 . 如图,在四棱锥
中,底面
是正方形,
底面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/629b903f-85aa-4c50-8051-b688d7420cdb.png?resizew=143)
(1)求证:平面
平面
;
(2)若点
为
中点,求
(ⅰ)点
到直线
的距离;
(ⅱ)直线
与直线
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf109530d399774ae2465fc324abffb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/629b903f-85aa-4c50-8051-b688d7420cdb.png?resizew=143)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(ⅰ)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
(ⅱ)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c884b508394b3ab50734b584d9ec783c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
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5 . 已知正四棱柱
中,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/97c094c7-3a19-4ec8-9610-db8d823ba7ad.png?resizew=116)
(1)求证:
;
(2)求平面
与平面
的夹角的余弦值;
(3)在线段
上是否存在点
,使得平面
平面
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c3defdd4d0c665d55184b84a7eb316f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66111d87f500aea4aeccb73b0ce7841a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/27/97c094c7-3a19-4ec8-9610-db8d823ba7ad.png?resizew=116)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/417104247ce266ae42c3a9860f387272.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9a248d1d22e1c29cfbce96b32e2206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d638516fee0dc3251d384400f478715.png)
(3)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc492b4bf027e8eeba9c08ecebb50f4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfa70b6554a9c50365435afc5742193c.png)
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名校
解题方法
6 . 如图,在三棱柱
中,
为
中点,四边形
为正方形.
平面
;
(2)再从条件①、条件②这两个条件中选择一个作为已知,求
(ⅰ)直线
到平面
的距离;
(ⅱ)直线
与平面
所成角的正弦值.
条件①:
;条件②:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83206a810e50309b06147efbb60fd10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
(2)再从条件①、条件②这两个条件中选择一个作为已知,求
(ⅰ)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
(ⅱ)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7935fe3125f247b7bea4f065ce9ad985.png)
条件①:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7870cee007535b979d35bc7feab75616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eabd2314dbe8bf1ef6e37a7befbb0c61.png)
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7 . 在平行六面体
中,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68fcb4a36ab923a64c77222c5959ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55b2ce97e1fd47e7a312391a6fd959ab.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
8 . 已知
是直线
上的两点,则直线
的倾斜角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64a33b7c8fee25b886aa5271c68cea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
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解题方法
9 . 已知数集
具有性质
:对任意的
,
,
,使得
成立.
(1)分别判断数集
与
是否具有性质
,并说明理由;
(2)若
,求
中所有元素的和的最小值并写出取得最小值时所有符合条件的集合
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc95c7daae935cccf8666865cba9eea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd446b1c54b898bba5260537f1b30db8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48d21d10197c3d078db9d1ac9293e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce133aca7a46be0dd5e055096addebac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1e76d1341e8e6bd89b7075150536bd.png)
(1)分别判断数集
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997bbd93dff19a5dba79bcd9d92f3129.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13470c4e9665748fdd20d0b181abc8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91a94ec87afbc073e077f2c453a304b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91fcc8350d2ed52931f48b8b5ca11215.png)
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2024-02-24更新
|
150次组卷
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2卷引用:北京市丰台区第二中学2023-2024学年高二下学期3月月考数学试题
名校
10 . 已知点是法向量为
的平面
内的一点,则下列各点中,不在平面
内的是( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-02-23更新
|
97次组卷
|
2卷引用:北京市丰台区第二中学2022-2023学年高二上学期10月月考数学试卷