名校
1 . 如图,在四棱锥
中,底面
为菱形,
平面
,
,
,
,
是
的中点,
在线段
上且
.
![](https://img.xkw.com/dksih/QBM/2021/10/15/2830043570380800/2833513853140992/STEM/09e165e7-a774-4e92-94da-0e2d4fd93b1c.png?resizew=275)
(1)用向量
,
,
表示向量
;
(2)求向量
的模长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.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/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb344d5cb0586981ad6974498897ebf2.png)
![](https://img.xkw.com/dksih/QBM/2021/10/15/2830043570380800/2833513853140992/STEM/09e165e7-a774-4e92-94da-0e2d4fd93b1c.png?resizew=275)
(1)用向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fe2d802f2b37e7db198c5a3c1df9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228f4ddbb8959f904d71259be7c6ab36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1395fa3420959a18d91b324adc622116.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3292381ac4e73f3192320ebe6acc104.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3292381ac4e73f3192320ebe6acc104.png)
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2021-10-20更新
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3卷引用:河北省省级联测2021-2022学年高二上学期第一次联考数学试题
河北省省级联测2021-2022学年高二上学期第一次联考数学试题河北省石家庄市二十三中2021-2022学年高二上学期第一次月考(10月)数学试题(已下线)期中考试模拟卷02-【一堂好课】2021-2022学年高二数学上学期同步精品课堂(人教A版2019选择性必修第一册)
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2 . 给出下列命题,其中是真命题的是( )
A.已知向量![]() ![]() ![]() |
B.若对空间中任意一点![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.平面![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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3 . 定义:设
是空间向量的一个基底,若向量
,则称实数组
为向量
在基底
下的坐标,已知
是空间向量的单位正交基底,
是空间向量的另一个基底,若向量
在基底
下的坐标为
,求向量
在基底
下的坐标,并求向量
的模.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955d3e36257ae2fffe46369ebb2f7364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f15a5e9b425566714a2604e8182c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b525d8c768efd801ab58bc4c0da9221e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1bfbd2ef51eaeb6e686e27cc95638e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/955d3e36257ae2fffe46369ebb2f7364.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8d2051594370095e72e173fd95888a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a9174ddc5bf2b76627676084ecda2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1bfbd2ef51eaeb6e686e27cc95638e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a9174ddc5bf2b76627676084ecda2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d567af011a49b2ab880c904dd2637b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1bfbd2ef51eaeb6e686e27cc95638e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8d2051594370095e72e173fd95888a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b1bfbd2ef51eaeb6e686e27cc95638e.png)
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4 . 在直三棱柱
中,
,
.点M,N分别是AC,AB的中点,过点C作平面
,使得
,
,若
,则
的值为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/d4da57fa-3e32-4707-8f5d-165e3c708545.png?resizew=146)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8684078379a9e6b209068e1de693af0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de40fe171c8d74b2a914dbe9bfe10f10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf5f4ca610ed56300a383dece0a5038.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f67e590df52154005c295e8db814f0a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd2320484fb9535aae762739f75520e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffbb47237959c76e5ee69148b11f7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73aa2f6da08428a893f3a376636c879e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/d4da57fa-3e32-4707-8f5d-165e3c708545.png?resizew=146)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知空间向量
,
,
不共面,且
,则x,y,z的值分别是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/524594bf0942ed86f56fc1eee120a81a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26a351759c36e8bd4aaac574cae73a0e.png)
A.2,1,2 | B.2,1,![]() |
C.1,![]() | D.l,![]() |
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2021-10-16更新
|
294次组卷
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2卷引用:人教B版(2019) 选修第一册 学习帮手 模块检测
6 . 在正三棱锥
中,点O为三角形BCD的中心,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c69611895c5a1ba5e11b63486e817a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
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7 . 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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8 . 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)
您最近一年使用:0次
2021-10-16更新
|
216次组卷
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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
9 . 对于不共面的三个向量
,
,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf67cd91976e3bb9ac944446bd13220.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/070d1ea22a92808dad7489438c239629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d67321ace1e6b3be0fc0e5e8130022.png)
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10 . 若
是空间向量的一组基底,向量
,
,则可以与
,
构成空间向量的另一组基底的向量是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8d2051594370095e72e173fd95888a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da709159aa1d305f442536681128867c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/705766829cd69d27d6de149556095a4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560ee2894ba8c5cee6633430cc8b3b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f1a8e551cba7ec9f451749f60e628d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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