名校
解题方法
1 . 如图,在直三棱柱
中,
,
分别为
,
的中点.
,求
的值;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a9ad711b25c36dae0c2a2cedff9954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78c45fb1bd3936fe41d53ea3ac772bf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e79d86dcb456ab7ae39a37c70b372848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
您最近一年使用:0次
2023-12-24更新
|
772次组卷
|
7卷引用:河北省邢台市质检联盟2023-2024学年高二上学期第四次月考(12月)数学试题
河北省邢台市质检联盟2023-2024学年高二上学期第四次月考(12月)数学试题河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(六)(已下线)高二数学开学摸底考 01(人教B版2019选择性必修第一册+第二册)-2023-2024学年高二数学下学期开学摸底考试卷贵州省六盘水市水城区2023-2024学年高二上学期12月质量监测数学试题广东省东莞市东华高级中学2024届高三一模数学试题吉林省部分名校2023-2024学年高二上学期期末联合考试数学试题新疆兵团地州学校2023-2024学年高二上学期期末联考数学试题
2023高三·全国·专题练习
2 . 如图四棱锥
,且
,平面
平面
,且
是以
为直角的等腰直角三角形,其中
为棱
的中点,点
在棱
上,且
.求证:
四点共面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d8f4270ac3c1844288bb5cb82e81ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/694e6bc99d14c7d9105928d3a0ccf0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36aae82d53f2a35d2f95f467bd5b76cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34f4ea9203ad9cd37c444cf1867c8746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3c11de81d6b7d9cb6b34f67aba11fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b3d919fe28e81cc33c049bd4956647.png)
![](https://img.xkw.com/dksih/QBM/2023/11/14/3367848286707712/3369243855331328/STEM/8132d4941e6a4f5aaef3629c23250e31.png?resizew=140)
您最近一年使用:0次
名校
3 . 如图,在正四棱锥
中,E,F分别为
的中点,
.
(1)证明:B,E,G,F四点共面.
(2)记四棱锥
的体积为
,四棱锥
的体积为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1443bfe022f648f813fb1e15b2d78b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de9fed9241141f03f50a109ff718a8cf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/1/7c55d54f-f787-4c6a-922d-e23a594a6325.png?resizew=152)
(1)证明:B,E,G,F四点共面.
(2)记四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83ddaa4ddb1938c804299f54f2f8ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4764374bd2fb78e59cd0b283637baeb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63055a5d6916f99d07fede49120753f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737b04ce09bc7e1ed86dc9b3c85203b.png)
您最近一年使用:0次
2023-11-10更新
|
399次组卷
|
8卷引用:河北省部分高中2023-2024学年高二上学期期中数学试题
名校
4 . 在空间直角坐标系中,已知点
,
,
.
(1)若A,B,C三点共线,求a和b的值;
(2)已知
,
,且A,B,C,D四点共面,求a的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f3d1559b293defb28b4570580ca1f83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f23ae5c8e69fe196f997ca7184ac66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5b6f5aaae52b812be8e8b4aae3197c.png)
(1)若A,B,C三点共线,求a和b的值;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce4430b8b9b0c78de693513a7f88915.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d2a3ce46b5ad55352501120930b51e.png)
您最近一年使用:0次
2023-10-24更新
|
316次组卷
|
5卷引用:模块二 专题1 利用空间向量对共线和共面问题的探究与应用 期末终极研习高二人教A版
(已下线)模块二 专题1 利用空间向量对共线和共面问题的探究与应用 期末终极研习高二人教A版(已下线)专题4 大题分类练(空间向量与立体几何)基础夯实练 高二期末广东省佛山市南海区大沥高级中学2023-2024学年高二上学期阶段检测一数学试题广东省江门市新会第一中学2023-2024学年高二上学期期中考试数学试题广东省江门市某校2023-2024学年高二上学期期中考试数学试题
2023高二·全国·专题练习
解题方法
5 . 已知
为空间9个点(如图),并且
,
,
.
,求证:
(1)
四点共面;
(2)
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/835a42aed01fa3cbce897f9ce23227ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab5a0a5347bb4a942331255cd5cf699b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed5a52c6b491bc8cc7b56083f9a755ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c2ef38a7acb8b1e50c581bc9330401.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb57de13c584f341fa67a829e431a91.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/3/326639ff-92ea-4825-b65b-7bf2eb43f965.png?resizew=158)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628ca06dd12a310d5fbdf6405c8a015.png)
您最近一年使用:0次
名校
6 . 如图,已知四棱锥
的底面为平行四边形,平面
与直线
、
、
分别交于点
、
、
,且满足
.点
在直线
上,
为棱
的中点,且直线
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/291ffae4-2525-4ee1-862b-846e34e612d4.png?resizew=167)
(1)设
,
,
,试用基底
表示向量
;
(2)若点
的轨迹长度与棱长
的比值为
,试讨论
是否为定值,若
为定值,请求出
,若
不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28121a595e617a54a3432bf5119b8773.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c59ab3c430815c8e1a5cef009876e6e.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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/558432772e71c0909a2764efbecaccf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/4/291ffae4-2525-4ee1-862b-846e34e612d4.png?resizew=167)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0c4233830b1dab99f34886748da7f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e5858d3f112ed294b312c485386f5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5c19f8de0ef5db66ec5061ef15813c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5401d7f4a297c8b097e74bdebaaa8570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de403aa12486a7f6e5e2a823200a2596.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
您最近一年使用:0次
2023-10-15更新
|
561次组卷
|
5卷引用:重庆市育才中学校2023-2024学年高二上学期10月月考数学试题
重庆市育才中学校2023-2024学年高二上学期10月月考数学试题江西省上饶市广信中学2023-2024学年高二上学期11月月考数学试题(已下线)专题01 空间向量与立体几何(5)(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)(已下线)第三章 空间轨迹问题 专题三 立体几何轨迹长度问题 微点2 立体几何轨迹长度问题综合训练【培优版】
7 . 已知空间三点
.
(1)求以
为邻边的平行四边形的面积;
(2)设
,若
四点共面,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab665d7ad1ae2d9e4245142b9ef10e6a.png)
(1)求以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5dc62e10004e73908091338362917da.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adaf9785ef588229b9f18ed1d5ede78d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
8 . 如图,在长方体
中,E,M分别是
,
的中点,
,
.
(1)若在线段
上存在一点
,使
∥平面
,试确定N的位置;
(2)在(1)的条件下,试确定直线
与平面
的交点F的位置,并求
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/30/a8a9ea23-944e-42ad-9170-9a1d548ccc58.png?resizew=187)
(1)若在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ebb05874eb3353d754af24c9974273e.png)
(2)在(1)的条件下,试确定直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/193b5b41994c2a4dfa5bb0bc984061cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
您最近一年使用:0次
9 . 如图所示,已知斜三棱柱
中,
,在
上和
上分别有一点M和N,且
,其中
.求证:
,
,
共面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daa303125d656565a0047cfdfe65d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04ae28f67e6f7346744ba73193e00b51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca31c862890af181c5603111a77c970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/18/38472757-e0ed-46c6-be59-87bd32db3fe6.png?resizew=157)
您最近一年使用:0次
2023-09-17更新
|
132次组卷
|
2卷引用:人教B版(2019)选择性必修第一册课本例题1.1.2 空间向量基本定理
名校
10 . 已知
是空间的一个基底,且
,
,
,
.
(1)求证:
,
,
,
四点共面;
(2)
能否作为空间的一个基底?若能,试用这一基底表示
;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5401d7f4a297c8b097e74bdebaaa8570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c854abb7eb1bb8e09433eb6f22dc70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64be8f8016561b63843c72977eba7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee7443cc42d784c22523915501ad909.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01a492106de3a9a64755275e30ba16e0.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639cdeadbc9e566f81d65a0506823b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e723e57753f0a4fe1ef8ca1aee0e2117.png)
您最近一年使用:0次
2023-09-07更新
|
917次组卷
|
5卷引用:山西省金科大联考2023-2024学年高二上学期开学考试数学试题
山西省金科大联考2023-2024学年高二上学期开学考试数学试题四川省成都市新津区成外学校2023-2024学年高二上学期9月月考数学试题(已下线)高二上学期期中复习【第一章 空间向量与立体几何】十大题型归纳(拔尖篇)-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)广东省广州市第八十九中学2023-2024学年高二上学期10月月考数学试题(已下线)模块四 专题4 大题分类练 《空间向量与立体几何》基础夯实练