名校
解题方法
1 . 若
均为单位向量,下列结论中正确的是_______ (填写你认为所有正确结论的序号)
(1)若
且
,且
,则
的取值范围为
;
(2)若
且
,且
,则
的取值范围为
;
(3)若
且
对任意实数
恒成立,则
的最小值为
;
(4)若
且
对任意实数
恒成立,则
的最小值为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cc1f1ef9ad32eef62aefa4c3fc3d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae19a80b97d4dfd1be47844c02980d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3797ac9ea94855ed77cb9be5b4671874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d6f122739bfe3e5182375b585870a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c73388e5a836011f59e523130b0784.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cc1f1ef9ad32eef62aefa4c3fc3d6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae19a80b97d4dfd1be47844c02980d8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29119d4f3ee3426a24700ff7b4ba3e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d6f122739bfe3e5182375b585870a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93188fdb80dbd006ff8e940f048896a7.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960fffaf9d3cee05667705c83419380e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8891c4e0d2d98d3070164b4a48f5d692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c279eca88d292dd0573b49efae2e07f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/960fffaf9d3cee05667705c83419380e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8891c4e0d2d98d3070164b4a48f5d692.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2aafdbb391ae0050cef40c8d590cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
您最近一年使用:0次
解题方法
2 . 在四面体
中,
,
,
,设四面体
与四面体
的体积分别为
、
,则
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a8c3adfb5c3cb6dd9ba688856e2dd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90592be71b12efb676770f65d68596f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1bb96d6663c8cdbf43ba53e1505e1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f107bd06ad6af2ff8d5aaa9ace12d9a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae00abada46919dffcfb342971dcdabd.png)
您最近一年使用:0次
名校
解题方法
3 . 正三棱锥
中,底面边长
,侧棱
,向量
,
满足
,
,则
的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3da3fdf44b48a0d66b87441fc699cab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b396937ce186ccb792210cb7b852f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40ca854e782895e8f5f08a65dce610c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e6f98f23fea7db0f74897928024ca0.png)
您最近一年使用:0次
2024-04-01更新
|
1126次组卷
|
6卷引用:上海市浦东新区2024届高三下学期期中教学质量检测数学试卷
上海市浦东新区2024届高三下学期期中教学质量检测数学试卷(已下线)压轴小题5 空间向量中的最值问题江苏省姜堰中学2024届高三下学期阶段性测试(2.5模)数学试题(已下线)数学(上海卷01)(已下线)压轴题06向量、复数压轴题16题型汇总-1上海市吴淞中学2023-2024学年高二下学期第二次调研(5月)数学试卷
4 . 已知四面体
中,
,且
与平面
所成的角为
,则当
时,
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8c3e673f6942831b8431e44409689f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f31592afa0f6735b29d6c616ff567c.png)
您最近一年使用:0次
解题方法
5 . 在空间四边形
中,
,则下列结论中不一定正确 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/530b5da93a364201409d99a39f703717.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
名校
6 . 正四面体
棱长为6,
,且
,以
为球心且半径为1的球面上有两点
,
,
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82f462070bf390881ceee2519ac07604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e49a1538831e007a0e47ec5e1069bff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5128656ad9b18360970d3f50cace2a7.png)
A.24 | B.25 | C.48 | D.50 |
您最近一年使用:0次
2024-01-10更新
|
1327次组卷
|
9卷引用:辽宁省五校联考2023-2024学年高二上学期1月期末数学试题
名校
7 . 正方形
的边长为12,其内有两点
、
,点
到边
、
的距离分别为3,2,点
到边
、
的距离也是3和2.现将正方形卷成一个圆柱,使得
和
重合(如图).则此时
、
两点间的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2024-01-04更新
|
856次组卷
|
8卷引用:上海市崇明中学2023-2024学年高二上学期期中考试数学试题
上海市崇明中学2023-2024学年高二上学期期中考试数学试题广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(一)江西省上饶市婺源天佑中学2023-2024学年高二上学期期末模拟数学试题上海市松江二中2023-2024学年高二上学期期末考试数学试题(已下线)专题2 用空间向量解决立体几何问题江西省临川第一中学2023-2024学年高二下学期第一次月考数学试卷(已下线)高二上学期期末考点大通关真题精选100题(1)(已下线)第8题 由空间距离求夹角(压轴小题)
2023·全国·模拟预测
名校
8 . 如图,直三棱柱
中,
为
的中点,
为线段
上的动点,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd23d99a40b6378a31fccfae692b3c5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/2/1a7d4ecc-38c3-4af5-bf0d-c8313da3bf51.png?resizew=136)
A.不存在点![]() ![]() |
B.![]() ![]() |
C.当![]() ![]() ![]() |
D.平面![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
9 . 在平行六面体
中,
,
,若
,其中
,
,
,则下列结论正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991451c5002137302527700e195220e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb66690bc5b8123d5eafe781d3c9a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d472051d1f6bce23c22a55c517515e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/900dea22ff8af341d08262f4b76c6953.png)
A.若点![]() ![]() ![]() | B.若![]() ![]() |
C.当![]() ![]() ![]() | D.当![]() ![]() ![]() |
您最近一年使用:0次
2023-11-23更新
|
506次组卷
|
4卷引用:安徽省滁州市九校2023-2024学年高二上学期期中考试数学试卷
安徽省滁州市九校2023-2024学年高二上学期期中考试数学试卷山东省菏泽市鄄城县第一中学2023-2024学年高二上学期12月月考数学试题(已下线)模块三 专题3 小题满分挑战练(1) 期末终极研习室(高二人教A版)(已下线)高二数学上学期第三次月考模拟卷(空间向量与立体几何+直线与圆的方程+圆锥曲线方程+数列)(原卷版)
名校
解题方法
10 . 已知四棱台
的下底面和上底面分别是边长为4和2的正方形,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/9/9155d6d8-6505-4f66-a083-82bebd06e5d4.png?resizew=188)
A.侧棱![]() ![]() ![]() ![]() |
B.若E为![]() ![]() ![]() ![]() ![]() |
C.![]() |
D.设![]() ![]() ![]() |
您最近一年使用:0次
2023-11-16更新
|
446次组卷
|
3卷引用:湖北省鄂东南省级示范高中教育教学改革联盟学校2023-2024学年高二上学期期中联考数学试题