1 . 如图,在空间直角坐标系
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/a2238804-d1bf-4d03-b483-12364b65f957.png?resizew=163)
(1)求向量
在向量
上的投影的数量.
(2)是否存在实数
,使得点
,
,
,
共面?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/735f4097109e3d66904227b87be47958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f73374a38242eac06517554b080798c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5ad34c568d275e4e0dd965549568647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0140db15921bab61aaecc0e79d7aec2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c136d1e90201d76e6e617a74b7d037e5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/15/a2238804-d1bf-4d03-b483-12364b65f957.png?resizew=163)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d792a2aa25763e14cc2863be3887000.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5a51e65e9b56a9970de33ead263a9.png)
(2)是否存在实数
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2 . 已知空间向量的一组基底
,
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15794d0b1dfa2f19e7b49e08e2df6ede.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8d2051594370095e72e173fd95888a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ccbe20a27a124f25fa60ec4b276a964.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5aa846a5b7c96fe2ce665eb1ea5f0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7557713682c09ec526718378189f9f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b6fc7e4e457a179af628d22d7b1dff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15794d0b1dfa2f19e7b49e08e2df6ede.png)
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2卷引用:人教B版(2019) 选修第一册 学习帮手 第一章 1.1.2 空间向量基本定理
3 . 已知长方体
中,点Q是BC上的动点,点P是
上的动点,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/16cf3a9c-ef9b-4a1f-baa7-5bb5e34ab297.png?resizew=168)
(1)求
;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f121eabff3c62c1a196d9ca5f6f83f0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad1a56baf43ffdf67bc8460856e31fec.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/16cf3a9c-ef9b-4a1f-baa7-5bb5e34ab297.png?resizew=168)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f00d06966913f9a4b898a424d1fc553f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88f9e65a23e8f2d0b418001f4039ac9.png)
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21-22高二·全国·课后作业
4 . 已知空间中四个不共面的点O、A、B、C,若|
|=|
|,且cos
,
cos
,
,则sin
,
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d494ff403fd5387a22860472080f8ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6067107911c9d1fc118497cdfddb1bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1440be451908d542b7955b06bf9e80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a80f0c3f7b7515c3de11593e2fad1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1440be451908d542b7955b06bf9e80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73760aef8ac320fb4cbfeb29b9191e5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1440be451908d542b7955b06bf9e80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c565463d2f7d57d3dca3cdaafb9c9f1f.png)
A.1 | B.![]() | C.![]() | D.![]() |
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21-22高二·全国·课后作业
名校
5 . 已知
是平面
的一个法向量,
是直线
的一个方向向量,若
,
,则
与
的位置关系是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/485e4833e2bf56741c1f25cad0b6a392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c5829a48597e6f5be32df3ae31b07c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe69f75e4fdc85cfc8aa3774d399e14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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21-22高二·全国·课后作业
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6 . 如图,在平行六面体
中,AB=4,AD=3,
,∠BAD=90°,
,且点F为
与
的交点,点E在线段
上,有
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/876aeb00-11a6-49e9-a5cc-ed607fe9dc12.png?resizew=193)
(1)求
的长;
(2)将
用基向量
来进行表示.设
x
y
z
,求x,y,z的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5600c2061f6e12991bf271a4a3ab51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b735c72cfb59b24ec9c4aae288942252.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/020ebe1219437129358b986eb9e70bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a9e0317741e5248efae26481ff7072.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/22/876aeb00-11a6-49e9-a5cc-ed607fe9dc12.png?resizew=193)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b5a51e65e9b56a9970de33ead263a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc83519fb29b2f612923ae9764ae35e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f95011066f40e5154b750675e396a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280eab531a8c06d1638eec118cca7be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5e42ed3a63431c4be97dc292daa6bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4045e804dd60d76364f831e44f2362aa.png)
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313次组卷
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4卷引用:专题1.6 空间向量基本定理-重难点题型检测-2021-2022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1.6 空间向量基本定理-重难点题型检测-2021-2022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)3.1 空间向量及其运算(基础练+提高练)-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)吉林省松原市吉林油田高级中学2021-2022学年高二上学期期中数学试题(已下线)专题1.6 空间向量基本定理-重难点题型检测-2022-2023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)
21-22高二·全国·课后作业
名校
7 . 已知正方体ABCD﹣A1B1C1D1的棱长为a,AC1与BD1相交于点O,则有( )
A.![]() | B.![]() |
C.![]() | D.![]() |
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3卷引用:专题1.4 空间向量的数量积运算-重难点题型检测-2021-2022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1.4 空间向量的数量积运算-重难点题型检测-2021-2022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)辽宁省沈阳市东北育才学校2015-2016学年高二上学期第二次段考数学试题(理科)广东省梅州市大埔县虎山中学2023-2024学年高二上学期期中数学试题
21-22高二·全国·课后作业
8 . 已知正方体ABCD﹣A′B′C′D′的边长为a.
(1)求
;
(2)求
;
(3)求
.
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e46def0a549d6732ba8198ae0f5e58.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10e6896af9c14dafb076252322180e7.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d4cbd14ea52d472488ef9972da2de6.png)
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21-22高二·全国·课后作业
9 . 如图:在平行六面体ABCD﹣A1B1C1D1中,点M是线段A1D的中点,点N在线段C1D1上,且
,∠A1AD=∠A1AB=60°,∠BAD=90°,AB=AD=AA1=1.
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779686212943872/2828005467619328/STEM/61186829-b087-46f9-b9bd-3442b9face38.png?resizew=330)
(1)求满足
的实数x、y、z的值.
(2)求AC1的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c4fbf02e6b69b31df52d176ba81fba.png)
![](https://img.xkw.com/dksih/QBM/2021/8/5/2779686212943872/2828005467619328/STEM/61186829-b087-46f9-b9bd-3442b9face38.png?resizew=330)
(1)求满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/087545465b99c586175ec6803ad933ee.png)
(2)求AC1的长.
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3卷引用:专题1.4 空间向量的数量积运算-重难点题型检测-2021-2022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1.4 空间向量的数量积运算-重难点题型检测-2021-2022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)河南省中牟县第三高级中学2022-2023学年高二上学期第一次月考数学试题山东省济南市莱芜区莱芜凤城高级中学2023-2024学年高二上学期10月月考数学试题
21-22高二·全国·课后作业
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10 . 如图,四棱锥
的各棱长都为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/96717595-53f8-4173-b202-daff21a6f231.png?resizew=191)
(1)用向量法证明
;
(2)求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/31/96717595-53f8-4173-b202-daff21a6f231.png?resizew=191)
(1)用向量法证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5d56d8170b764b80a672cd6c861921.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae650fd9373cde94ef2e4e6103478fd5.png)
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4卷引用:专题1.4 空间向量的数量积运算-重难点题型检测-2021-2022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1.4 空间向量的数量积运算-重难点题型检测-2021-2022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1.4 空间向量的数量积运算-重难点题型检测沪教版(2020) 选修第一册 同步跟踪练习 第3章 3.1 第2课时 空间向量的数量积运算与共线山东省聊城市第二中学2022-2023学年高二上学期开学考试数学试题