名校
解题方法
1 . 正四棱台
是
的中点,在直线
上各取一个点P、Q,使得M、P、Q三点共线,则线段
的长度为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3cc5ef92d20f1062e90fb8c92a025c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74f4c17021e82edbe97e8a7b60907aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2023-12-19更新
|
706次组卷
|
5卷引用:上海市嘉定区2024届高三一模数学试题
上海市嘉定区2024届高三一模数学试题广东省广州市中山大学附中2024届高三上学期第一次调研数学试题江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)(已下线)专题2 用空间向量解决立体几何问题(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
名校
解题方法
2 . 点P是长方体
内的动点,已知
,Q是平面BC₁D上的动点,满足
,则
的最小值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aecba711ddb1b9181652eceb18fb038b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d14c6959273338a048b023805cce80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
您最近一年使用:0次
2023-11-11更新
|
429次组卷
|
5卷引用:浙江省浙南名校联盟2023-2024学年高二上学期11月期中联考数学试题
浙江省浙南名校联盟2023-2024学年高二上学期11月期中联考数学试题浙江省浙南名校联盟2023-2024学年高二上学期期中联考数学试题浙江省金华市武义第一中学2023-2024学年高二上学期11月检测2数学试题(已下线)3.3 空间向量的坐标表示(九大题型)(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)压轴小题5 空间向量中的最值问题
名校
3 . 如图所示的几何体
中,
和
均为以
为直角顶点的等腰直角三角形,
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/2020/5/26/2471193277857792/2471708998156288/STEM/671926a565504cf289445e9b734199ea.png?resizew=237)
(1)求证:
;
(2)求二面角
的大小;
(3)设
为线段
上的动点,使得平面
平面
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be89b9d1709d7974a108142c5fa2ccec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a855335176fc36a15017f50a8561348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/099dd87a526391f830ac2a11e7d7ad56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bd02e0adeae92ba9526261b1baf797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52bbb16f9380dd62d556480a3944be31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66418ef39d3081d89411a4907d8599f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fdf241efcd0c8026d188fad5a5ba4e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/2020/5/26/2471193277857792/2471708998156288/STEM/671926a565504cf289445e9b734199ea.png?resizew=237)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5ffe436f8eb53a211abf95baed8ca9.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd548dfcef01e147e4dce25bd384f9b9.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df0cf60b84dcb4baf97c39fe659e08a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910043595f4eed0c5b2a2246bec3664c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
您最近一年使用:0次
2020-05-27更新
|
2399次组卷
|
16卷引用:2020届天津市河西区高考一模数学试题
2020届天津市河西区高考一模数学试题山东省新泰市第一中学老校区(新泰中学)2020-2021学年高二上学期第一次月考数学试题山东省潍坊市寿光市现代中学2020-2021学年高二(上)期中数学试题山东省寿光现代中学2020-2021学年高二11月月考数学试题(已下线)考点29 空间向量解决空间直线、平面位置关系-备战2021年新高考数学一轮复习考点一遍过(已下线)专题1.3 空间向量及其运算的坐标表示-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第一册)辽宁省大连市红旗高级中学2020-2021学年高二上学期期中数学试题海南省北京师范大学万宁附属中学2021-2022学年高二上学期第一次月考数学试题天津市南开中学2022-2023学年高三上学期10月阶段性统一练习(一)数学试题广西玉林市博白县第四中学(博白县中学书香校区)2022-2023学年上学期高二9月月考数学试题广东省台山市第一中学2022-2023学年高二上学期期末数学试题(已下线)第01讲 空间向量及其运算(6大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)广东省深圳市福田区外国语高级中学2023-2024学年高二上学期期中数学试题(已下线)专题01 空间向量与立体几何(5)(已下线)高二数学第一学期期期末押题密卷03卷(已下线)第3章 空间向量及其应用 单元综合检测(难点)-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)
2016高二·全国·课后作业
4 . 如图,已知
、
、
、
、
、
、
、
、
为空间的
个点,且
,
,
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/2016/11/15/1836136229879808/1826268636012544/STEM/2022ebbeb0664162b3f84a7ed49038ac.png?resizew=167)
求证:(1)
、
、
、
四点共面,
、
、
、
四点共面;
(2)
;
(3)
.
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/c8fa5b04e30e48868fe132789b807597.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/3066e7be6d7c4c518443aac35ebc6fc5.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b91007e2ea5e433e95db20f4365af044.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/97903bb1c17f421d99f9d22a60f06e1a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/04d375abd23446d49614ae0320e80084.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b5a2daa15b914c598c2eab346ad7223e.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/33f3cc1423584e0dbcb2758c3e25432d.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/0b593aab85fb4dbcb2ebdf05a19793da.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/855db6b1d0d84981842248c6e4474b0e.png?resizew=19)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/0dbdef66d115422081bc2e5a32f48d7c.png?resizew=12)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/847f57351bde4581abef8a8eca1c6630.png?resizew=72)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/c6b86275082f489cbaca3001edb878c6.png?resizew=74)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/cba340111acb4e49b35a90810589fa18.png?resizew=77)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/ae8730bc42424af6af4187c0829e1322.png?resizew=115)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/f1055c0362da4a4fbde3e599db2ebaeb.png?resizew=116)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/3ef175e21b1b4b148b88a747da214799.png?resizew=37)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/4f3b0d4465694c178a6a044b9be25f3a.png?resizew=42)
![](https://img.xkw.com/dksih/QBM/2016/11/15/1836136229879808/1826268636012544/STEM/2022ebbeb0664162b3f84a7ed49038ac.png?resizew=167)
求证:(1)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/3066e7be6d7c4c518443aac35ebc6fc5.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b91007e2ea5e433e95db20f4365af044.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/97903bb1c17f421d99f9d22a60f06e1a.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/04d375abd23446d49614ae0320e80084.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/b5a2daa15b914c598c2eab346ad7223e.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/33f3cc1423584e0dbcb2758c3e25432d.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/0b593aab85fb4dbcb2ebdf05a19793da.png?resizew=17)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/855db6b1d0d84981842248c6e4474b0e.png?resizew=19)
(2)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/EXPLANATION/8fe0f5e54a904f04abfa0fdf835415be.png?resizew=68)
(3)
![](https://img.xkw.com/dksih/QBM/2016/11/29/1826268635201536/1826268636012544/STEM/26aac0e0723242a8984e34736049ce88.png?resizew=76)
您最近一年使用:0次