名校
解题方法
1 . 如图,正方体
的棱长为2,
为
的中点,
为棱
上的动点(包含端点),则下列结论正确的是( )
![](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/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.存在点![]() ![]() | B.存在点![]() ![]() |
C.四面体![]() ![]() | D.点![]() ![]() ![]() |
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2024-01-31更新
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291次组卷
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4卷引用:四川省攀枝花市普通高中2023-2024学年高二上学期教学质量监测数学试题卷
四川省攀枝花市普通高中2023-2024学年高二上学期教学质量监测数学试题卷四川省内江市第六中学2023-2024学年高二下学期入学考试数学试题四川省眉山市彭山区第一中学2023-2024学年高二下学期4月月考数学试题(已下线)第二章 立体几何中的计算 专题六 空间定值问题 微点1 立体几何中的定值问题综述及定长、定距问题【培优版】
解题方法
2 . 下列结论正确的是( )
A.若向量![]() ![]() ![]() ![]() ![]() ![]() |
B.已知平面![]() ![]() ![]() ![]() ![]() ![]() |
C.若直线![]() ![]() ![]() ![]() ![]() |
D.若向量![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
3 . 三棱柱
中,
为
中点,点
在线段
上,
.设
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/6b6519bd-4c70-41ea-9b11-f52b8dc64222.png?resizew=192)
(1)试用
,
,
表示向量
;
(2)若
,
,求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af1699c5592f30ea1e279414c63f15e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f386f5b56b07b96f2600da1be15414a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/6b6519bd-4c70-41ea-9b11-f52b8dc64222.png?resizew=192)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5fd85ee3df1c1c7c499c9f500c99c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af2626608f61a4cfbb86494bd6df0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2024-01-25更新
|
124次组卷
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2卷引用:四川省凉山州2023-2024学年高二上学期期末检测数学试卷
4 . 如图,四面体
的所有棱长均为2,D,F分别为
,
的中点,且点E为
的三等分点(靠近点B).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/1e969929-e6e1-422d-8245-f4856eea71f3.png?resizew=160)
(1)设向量
,
,
,用
,
,
表示向量
;
(2)求点D到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334a5773c8d24f29ec3231075170e4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77e9c89b7275b0c1a9af5c9a72e5968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/1e969929-e6e1-422d-8245-f4856eea71f3.png?resizew=160)
(1)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd0a772a009eec08ec6d50a59eae67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7824b7ecd7d62f8a76a05c88bfd6693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95e02cdf7ad2557cd1e92a8b438a9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8c53645db602c72b00b599c2c0ff97.png)
(2)求点D到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3747e528a1e8d45668ccf835c0175a73.png)
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2024-01-22更新
|
137次组卷
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4卷引用:四川省巴中市2023-2024学年高二上学期期末考试数学试卷
四川省巴中市2023-2024学年高二上学期期末考试数学试卷四川省遂宁市2023-2024学年高二上学期期末质量监测数学试题四川省雅安市2023-2024学年高二上学期期末教学质量检测数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点3 空间向量基底法(三)【基础版】
23-24高二上·北京·期中
名校
5 .
,
是直线
上的两点,若沿
轴将坐标平面折成
的二面角,则折叠后
、
两点间的距离是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc6434a2032cd3b56d51e440d494bdd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658cbf168f4d699b8fb8f02be5167c44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a2b4c212450b2a0f77e042c8da13dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.6 | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
6 . 已知
,
,
,若
,
,
三向量共面,则实数λ等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5720aa4c442c639ab3f4af0f34979595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6aa75526f786478ba209cfe013317ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e78ffd28317b1e685bc0c9376ab49933.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff409cd3886c767afb13c9a869c5f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6570cd7c2f81c9fcffd2c64664f1564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d8e782e9687f2e6276a8541ff8dcf7.png)
A.1 | B.2 |
C.3 | D.4 |
您最近一年使用:0次
2024-03-05更新
|
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15卷引用:四川省平昌县第二中学2023-2024学年高二上学期第一次月考数学试题
四川省平昌县第二中学2023-2024学年高二上学期第一次月考数学试题广东省潮州市潮安区凤塘中学2023-2024学年高二上学期期中数学试题山东省青岛第五十八中学2023-2024学年高二上学期期中考试数学试卷广东省东莞市实验中学2023-2024学年高二上学期期中数学试题黑龙江省鸡西市虎林高级中学2023-2024学年高二上学期第一次月考数学试题山东省济宁市泗水县2023-2024学年高二上学期期中数学试题山东省日照市国开中学2023-2024学年高二上学期第一次月考数学试题山东省菏泽市第一中学八一路校区2023-2024学年高二上学期12月月考数学试题河南省信阳市商城县上石桥高级中学2023-2024学年高二上学期12月月考数学试题江苏省清河中学2022-2023学年高二下学期3月阶段测试数学试卷(已下线)第六章 空间向量与立体几何(单元重点综合测试)-2023-2024学年高二数学单元速记·巧练(苏教版2019选择性必修第二册)(已下线)3.1 空间向量及其运算(八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)上海市宝山区上海师大附属宝山罗店中学2023-2024学年高二下学期第一次诊断性测试(3月)数学试卷江苏省连云港市厉庄高级中学2023-2024学年高二下学期2月学情检测数学试卷江苏省宿迁市沭阳如东中学2023-2024学年高二下学期阶段测试(三)数学试卷
7 . 四棱柱
的六个面都是平行四边形,点
在对角线
上,且
,点
在对角线
上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/4d6704cd-d846-48a0-8dfc-3b921517bb0e.png?resizew=185)
(1)设向量
,
,
,用
、
、
表示向量
、
;
(2)求证:
、
、
三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7edc594bc197a4f8ae571df31d22b56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eb97aff0960e2640314888a38e7169c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ae4af331bca6587521e6dd4212f78d1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/6/4d6704cd-d846-48a0-8dfc-3b921517bb0e.png?resizew=185)
(1)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7b9d8a08fc52c31cc1a7f527d18b55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184359fe3cadc363cf4ebe586c2b3db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b0ff98fe5e0a913ebecda552acc6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ef300fccd1d15cfd5556f9d742e12f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a53766326ff2736199a9318970f1603c.png)
(2)求证:
![](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/e5b3bd5e6bc2a0a277d279bb01af9584.png)
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2024-02-27更新
|
249次组卷
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7卷引用: 四川省泸县第五中学2023-2024学年高二上学期第一次月考试数学试题
四川省泸县第五中学2023-2024学年高二上学期第一次月考试数学试题(已下线)3.1 空间向量及其运算(已下线)高二上学期第一次月考解答题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)专题 01 空间基底及综合应用(3)(已下线)专题01 空间向量与空间位置关系【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)(已下线)专题 01 空间基底及综合应用(4)(已下线)3.2 空间向量基本定理(五大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
解题方法
8 . 已知斜棱柱
中,
,
.设
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/2f22d8ff-5b0c-4715-9280-98af323f674c.png?resizew=136)
(1)用基底
,
,
表示向量
,并求
;
(2)求向量
与向量
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead0e8eadfdcefa334953e88864f424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d13ecb54b1006051d2561327aa4755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/2f22d8ff-5b0c-4715-9280-98af323f674c.png?resizew=136)
(1)用基底
![](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/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2854c67a40773c10bf0a89479d36a0df.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
您最近一年使用:0次
名校
解题方法
9 . 正方体
的棱长为
,
,
,
分别为
,
,
的中点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/50d5fe9e-3d4e-47f9-bf16-7d26ca75f63b.png?resizew=152)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/21/50d5fe9e-3d4e-47f9-bf16-7d26ca75f63b.png?resizew=152)
A.![]() |
B.直线![]() ![]() ![]() |
C.点![]() ![]() ![]() |
D.直线![]() ![]() |
您最近一年使用:0次
2024-01-21更新
|
288次组卷
|
2卷引用:四川省绵阳市南山中学2023-2024学年高二上学期12月月考数学试题
名校
10 . 在平行六面体
中,
分别是
的中点,
是线段
上的两个动点,且
,以
为顶点的三条棱长都是1,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9e3f3f09715fd737324ea48c3696485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b8bcc3fdc20609cac1a7e635a5d869c.png)
A.![]() ![]() | B.![]() |
C.三棱锥![]() | D.三棱锥![]() ![]() |
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2024-01-20更新
|
629次组卷
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2卷引用:四川省成都市玉林中学2023-2024学年高二上学期期末模拟数学试题(一)