2024高三·全国·专题练习
解题方法
1 . 已知向量
、
是平面
内的两个不共线的向量,
,
,求平面
的一个法向量
的坐标.
![](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/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fec47d876cbc0404e3c764656863a4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8385074657a9ce96b780ace167f2ed1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
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2024高三·全国·专题练习
解题方法
2 . 已知在正四棱柱
中,
,
,E为
的中点,F为
的中点.求证:
(1)
且
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8395ad704eb0d1e66f7c2e1558de34ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1025ae64ab3bbc38c0a9adbb8ef73e13.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db68c2e813588fdb7357757199992350.png)
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2024高三·全国·专题练习
解题方法
3 . 如图,在正方体
中,
,
,
,点M,N分别是
,
的中点.
(1)试用
,
,
表示
.
(2)求证:
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a08f3a88dffed011df93d1d606a08ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f8173bb7787b6b107acfe767dd1d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/232311b4261c36b659555a07bfa00f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/d1ed7a47-813c-483a-a098-5d06cabb43a5.png?resizew=171)
(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)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
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名校
4 . 已知空间向量
.
(1)求
;
(2)判断
与
以及
与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a9be0ea19a65bf3f4e2a45cb84575a7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/884e8f2d5835771fd49093a6709be3a0.png)
(2)判断
![](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/7b76118bdca6c463cfb19b66f30281c4.png)
您最近一年使用:0次
名校
5 . 在正四棱柱
中,
,
是棱
上的中点.
(1)求证:
;
(2)异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b66218bbfb24acee762d795831e42c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/28/56f1fa7d-2b62-4c27-ab33-8062918930d5.png?resizew=130)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ab924e3692515bd8be4c36472a959a.png)
(2)异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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2023-10-20更新
|
2746次组卷
|
16卷引用:北京市丰台区2022-2023学年高二上学期数学期末练习数学试题
北京市丰台区2022-2023学年高二上学期数学期末练习数学试题四川省雅安市雅安中学2022-2023学年高二下学期期中数学(理)试题第一章 空间向量与立体几何 (单元测)河南省郑州市基石中学2022-2023学年高二下学期期中数学试题(已下线)第三章 空间向量与立体几何(基础巩固检测卷)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)北京市朝阳区东北师范大学附属中学朝阳学校2023-2024学年高二上学期第一次学习质量监测与反馈数学试题湖南省长沙市德成学校2023-2024学年高二上学期10月月考数学试题山西省运城市景胜中学2023-2024学年高二上学期10月月考数学试题(A卷)河南省三门峡市渑池县第二高级中学2023-2024学年高二上学期第二次月考(11月)数学试题(已下线)考点12 空间角 2024届高考数学考点总动员 【讲】福建省仙游县枫亭中学2022-2023学年高二下学期期中考试数学试题江苏省南通市如皋中学2024届高三创新实验班夏令营数学试题海南省川绵中学2023-2024学年高二上学期10月第一次月考数学试题广东省佛山市顺德德胜学校2023-2024学年高二上学期期中数学试题广西壮族自治区桂林市灵川县广西师大附中2023-2024学年高二上学期段考(期中)数学试题湖南省张家界市民族中学2023-2024学年高二上学期第二次月考数学试题
解题方法
6 . 已知
,
,
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11c56d479e3620d764eccab05fe0a1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e076b91a9178217532e11c496400e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bc8444d63d1ca92651c62fe9b220859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea730233033e2fca0bce6a369a32582f.png)
您最近一年使用:0次
解题方法
7 . 已知AB,AC分别是平面
的垂线和斜线,BC是AC在
内的射影,
且
.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1754786a3367aca3da18ee3316e5b968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3777318aa3fbdee09cfeeea971e8fcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95e692badf11ca5ac25104a166f4467.png)
您最近一年使用:0次
解题方法
8 . 如图,已知平面
,
,直线
平面
,且
平面
.求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be509ef5101aae24609ff9941cb246fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa807136194c18d3ac58902c67f9333.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/65bb0b48-a810-4828-8f53-423ccc862ef7.png?resizew=164)
您最近一年使用:0次
解题方法
9 . 已知两条不重合的直线m,n和平面
都垂直.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0205571fa39f343ee5749b78d466bf0.png)
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10 . 如图,已知正方体
中
,
的坐标分别为
,
,
,
.分别求平面
与平面
的一个法向量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65183d238c9bc2be73770717d890683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a42bc893aeabafad84da3e66e73f885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b11c6835301f2b6b8b3f50797dc434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5738e712c599c54aebca0d4a3d9fcf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/359da7e284844965b9bb9121f5c43bfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ad7c7bdb5c5cfa477eb4f5ea57d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/20/effc782c-e29f-4170-9e09-6ea43e169a92.png?resizew=178)
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