名校
1 . 已知空间向量
,
,
.
(1)若向量
与向量
垂直,求x的值;
(2)在(1)的条件下判断向量
,
,
是否共面?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5ddddabc3bd62f1f5561df866f4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba5fb8d5433ae8f9ae586254bb43e0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90bf9270e5dbaec7b9486f45368770b5.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b0c233484ce028819ebd0c86b75a92b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(2)在(1)的条件下判断向量
![](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)
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名校
2 . 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)
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2023-11-10更新
|
399次组卷
|
8卷引用:湖南省常德市部分学校2023-2024学年高二上学期11月联考数学试题
名校
解题方法
3 . 如图所示,在四棱锥
中,
平面
,
,
,
,
.过点
作四棱锥
的截面
,分别交
,
,
于点
,
,
,且
,
.
为
的中点,求实数
的值;
(2)若
,求平面
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a923784f083b7f4777891afe06b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8d0e8404f347a0eb4c76f4d25d9bdac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.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/0c952710701568f5b87630c1f914cc00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c62040d758136eeb9af6052b72d9b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441809d6ce2df21a85b390cdce9b1112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72d8a3dc6cb93171ee20567b5440775.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2023-03-18更新
|
322次组卷
|
3卷引用:湖南省株洲市第一中学2021-2022学年高二下学期期中考试数学试题
21-22高二·湖南·课后作业
解题方法
4 . 已知A,B,C三点不共线,对空间任意一点O,当
(其中
)时,点P是否与A,B,C共面?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cc5c5670877248cec1f91e8d4eda25b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
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21-22高二·湖南·课后作业
5 . 阅读“多知道一点:平面方程”,并解答下列问题:
(1)建立空间直角坐标系,已知
,
,
三点,而
是空间任意一点,求A,B,C,P四点共面的充要条件.
(2)试求过点
,
,
的平面ABC的方程,其中a,b,c都不等于0.
(3)已知平面
有法向量
,并且经过点
,求平面
的方程.
(4)已知平面
的方程为
,证明:
是平面
的法向量.
(5)①求点
到平面
的距离;
②求证:点
到平面
的距离
,并将这个公式与“平面解析几何初步”中介绍的点到直线的距离公式进行比较.
(1)建立空间直角坐标系,已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f6f9d8550d619061ab0ba1105ec6a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adf322f683d50ecd3c7d4d5996122726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b82ad92798b264062c062f4a9a1a5c.png)
(2)试求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd3ea554707fa3fc12fc9de51c94e4fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5622d4be6bba8c7a6851dc082ef34fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1f4b53c90e4c31dd35b4bb548c5193.png)
(3)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b163c34a920cb649829c376e7870007a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b5103a4c35ab0c395c68690a300023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(4)已知平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e0ae1c14104ee9985e3ba31c604531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(5)①求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae715c996c1a6b5e35a3807c671bd6e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
②求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e874a5821372c21a768cd1f5e20536d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a0cbd6b024b3fdff2f5fb5602da1a3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c828e62664e7373ed1f6dde8aa9653c.png)
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21-22高二·湖南·课后作业
6 . 如图,四边形ABCD是平行四边形,过平面AC外一点O作射线OA,OB,OC,OD,在四条射线上分别取点E,F,G,H,并且使
.求证:E,F,G,H四点共面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0589096dce4ed16d7b1f78b87d9bcf.png)
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2022-03-05更新
|
366次组卷
|
6卷引用:2.3.2 空间向量运算的坐标表示
(已下线)2.3.2 空间向量运算的坐标表示(已下线)1.1.1空间向量及其线性运算(导学案) -【上好课】高二数学同步备课系列(人教A版2019选择性必修第一册)人教A版(2019)选择性必修第一册课本例题1.1 空间向量及其运算湘教版(2019)选择性必修第二册课本习题 习题2.3(已下线)专题01 空间向量及其运算压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)(已下线)第04讲 空间向量及其运算 (1)
7 . 已知空间中三点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b689f1ca95aa564df552377f287d7cb7.png)
(1)求
的面积;
(2)若点
在
三点确定的平面内,求x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b689f1ca95aa564df552377f287d7cb7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9952d46931a57a0afdfce610425244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
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2021-10-14更新
|
249次组卷
|
3卷引用:湖南省A佳大联考2021-2022学年高二上学期10月月考数学试题
19-20高二·全国·课后作业
名校
8 . 已知{
}是空间的一个基底,且
=
,
=
,
=
,试判断{
}能否作为空间的一个基底?若能,试以此基底表示向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0762365cf0afd8d6966d7d3407e2ade0.png)
;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae0bbc15c3f7f2edbb78ecfde40825d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed9e2c8c99360e21d4c8cf578cba1e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ba58d0939649c714b003758bd1cb7fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20ec3efaa6b6ff5769e8999df5714a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43fd2605b01b5a99ef1caeaa723b600b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12043fbdfadbf715bbc7969cdf71a907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0762365cf0afd8d6966d7d3407e2ade0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db46e5432459b458c7470407ce6ff71a.png)
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