解题方法
1 . 如图,已知棱长为
的正四面体ABCD,点
,
,
分别是
,
,
的中点,求下列向量的数量积:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/28/f56baf20-98be-49e0-9c88-db7a9de6a0f1.png?resizew=181)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21bfe273ec30b01f3245dfbf78b15083.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56aaa042299f80c1f135499e6855a1f9.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dfbe48e1b5e6d747134bbf9ff0a97a.png)
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解题方法
2 . 对任意实数
,
,
,
,
,
,试用向量知识证明下述结论:
,等号成立的条件是:
或
或存在实数a使
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54015ff5b49e3283901da1291b6b921d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6872ffb1934339c53c2c2282d5889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af68f652b4c13657ffddf3c9e7eb262b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa224ed9be8766a4d0b5138bd57de0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a26b96592c3b1de759158fdaf05603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc6133ac108a13395d26eb3db1213b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9e96709acc623fe7d4c0fd5b8b4c7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46a24785fa8c20e112f034a2c4715ef.png)
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3 . 设O为坐标原点,向量
,
,
,点
在直线
上运动,求
取得最小值时点Q的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97a9b9360505c80e01d822d9e5b2bb5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc618c0a61d175571007a537438d15b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6847e3137c6ea335e3309f641a26593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d871b0b46194d7300950e04f085533d2.png)
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解题方法
4 . 已知在空间四边形
中,
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62d52be7c6e607972b4cf8ccbf58436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22bebf68c92f3fc0de750330b001df56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/846bbe6e9646cae074a24c0dffc6d8f3.png)
您最近一年使用:0次
解题方法
5 . 设ABCD是空间四边形,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c20185f401a16a6e163ff452df9cee02.png)
您最近一年使用:0次
6 . 如图,长方体
的棱长
,
,
.
(1)求
;
(2)求
与
所夹角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/22/88d03d4c-71da-4fad-ac22-aa4032166dc0.png?resizew=173)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3e2f28ac4cdcfc9d7bf852e66d7a6f6.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4781e3daa2c4e018ca0ae09bb56abc0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
您最近一年使用:0次
7 . 如图所示长方体
中,
是
的中点,
,
,求:
;
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/915f809f058c88b2d466ac141be18ce2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f19d96da5bbbb48f92e40e18484d0bc5.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fbda2603643ab97c361459a546a7002.png)
您最近一年使用:0次
2023-10-03更新
|
195次组卷
|
6卷引用:人教B版(2019)选择性必修第一册课本例题1.1.1 空间向量及其运算
人教B版(2019)选择性必修第一册课本例题1.1.1 空间向量及其运算(已下线)高二上学期期中复习【第一章 空间向量与立体几何】九大题型归纳(基础篇)-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)(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 空间向量的线性运算(考点清单)-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)高二上期中真题精选(压轴60题30个考点专练)【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)高二上期中真题精选(易错60题30个考点专练)【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)
解题方法
8 . 证明:在平面内的一条直线,如果它和这个平面的一条斜线在这个平面内的射影垂直,那么它也和这条斜线垂直.(三垂线定理)
您最近一年使用:0次
9 . 如图,为某种礼物降落伞的示意图,其中有8根绳子和伞面连接,每根绳子和水平面的法向量的夹角均为30°.已知礼物的质量为
,每根绳子的拉力大小相同.求降落伞在匀速下落的过程中每根绳子拉力的大小(重力加速度g取
,
,精确到0.01N).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f1b1bd0f94ae786c99ded377c0e79a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1550a63581b2594012f126867a025af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47bb3f35e3db7c1f3a3dd3eb20151b5f.png)
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10 . 如图,在平行六面体
中,
,
,
,
,
.求:
;
(2)
的长(精确到0.1).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598098f91b9ad36cf04a7f839761f93d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d97a83c7bc0b91016f61a43833042d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
您最近一年使用:0次
2023-09-19更新
|
350次组卷
|
3卷引用:人教A版(2019)选择性必修第一册课本例题1.1 空间向量及其运算
人教A版(2019)选择性必修第一册课本例题1.1 空间向量及其运算四川省成都市金牛区实外高级中学有限公司2023-2024学年高二上学期第一阶段考数学试题(已下线)专题01 空间向量的线性运算(考点清单)-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)