名校
解题方法
1 . 定义空间中既有大小又有方向的量为空间向量.起点为
,终点为
的空间向量记作
,其大小称为
的模,记作
等于
两点间的距离.模为零的向量称为零向量,记作
.空间向量的加法、减法以及数乘运算的定义与性质和平面向量一致,如:对任意空间向量
,均有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bcfdf754e71318fb8329b8e7c09264.png)
,
,
;对任意实数
和空间向量
,均有
;对任意三点
,均有
等.已知体积为
的三棱锥
的底面均为
,在
中,
是
内一点,
.记
.
(1)若
到平面
的距离均为1,求
;
(2)若
是
的重心,且对任意
,均有
.
(i)求
的最大值;
(ii)当
最大时,5个分别由24个实数组成的24元数组
满足对任意
,均有
,且对任意
均有
求证:
不可能对任意
及
均成立.
(参考公式:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c082be7f93f355e1ca70588a4a89aead.png)
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28fde0a8b4ec1e2fff42cee3fc54c0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28fde0a8b4ec1e2fff42cee3fc54c0f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49da589810153e2ec39ed656a2b61f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12de8a4f788ff23d36e74c811354779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53bcfdf754e71318fb8329b8e7c09264.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3ff5e2f25dfebafaf8db07712ff706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff47a4801df7bc7bce1cb52327a7b174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e0a953946d9e878aa017c7f24ffb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0714b48d55f6b0854fb90a4255bc49c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fa157b4f65f3a9aa1f7f82de02e99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e1e19465c82977a26ca6900622ee1bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/718ba76bf48024ca425948e470e60042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c761455094dc4913de76122017a243dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48ac6b0dda0647d7dad3287ce4ad258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d131fd570dc36b912396dc2dd06405c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4aeda1e642ce85f1c0394bc419bda8e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f49f84442a1b38f27ac977214cd4b688.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902a402a179a09f74f2391fb5cb4ae6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/247daad150250fc13a230d5375adda93.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab39849dc21c8c68cd5cde0911d5db23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61e6011a0717ef57516821d0407a656.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae3155971b2bb3c9d68b43e14b7186f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ffe9f4e3243bd760835af03fa7ffe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8c053ebe33366203ad0eca474760118.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d05f59bfd6b1f55920e73653bf87a46.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6ffe9f4e3243bd760835af03fa7ffe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db09e9844b90e46a6f2f5a710b6a3451.png)
(参考公式:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c082be7f93f355e1ca70588a4a89aead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2343b61be295955a2b9baea86202f32.png)
您最近一年使用:0次
2024-06-13更新
|
353次组卷
|
2卷引用:重庆市巴蜀中学校2023-2024学年高一下学期5月期中考试数学试题
2 . 如图,点
是四面体
的棱
的中点,点
是三角形
的重心,点
在线段
上,且
,设
,
,
,则下列等式成立的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/31fca225-6ba7-4e87-8a70-9c8e4f42dcba.png?resizew=162)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb802b0cd77d772dceff0d9ff6c879ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc16de84ba253ac1471602c3ed28b019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420ad6159fc091d6a5ffddf0676d2662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c2e7e9fd8519fd1c293cc577408263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a40f8ef7e3af00c41f85a20578afdb57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/31fca225-6ba7-4e87-8a70-9c8e4f42dcba.png?resizew=162)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
3 . 已知空间四边形
中,
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a54d6f2600370c3841017b1d030e630.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
4 . 如图,在平行六面体
中,底面
是边长为
的正方形,侧棱
的长为
,且
.求:
的长;
(2)直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1f9ec447356842c12da7c8ae1d2d8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c92b5799d12ea37de46d7c942ce7a9.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
您最近一年使用:0次
2024-01-20更新
|
190次组卷
|
9卷引用:重庆市长寿区八校联考2023-2024学年高二上学期期末检测数学试题(B卷)
重庆市长寿区八校联考2023-2024学年高二上学期期末检测数学试题(B卷)(已下线)期末押题卷01(考试范围:苏教版2019选择性必修第二册)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)人教A版(2019) 选择性必修第一册 新高考名师导学 第一章 复习参考题 1广东省广州中学2021-2022学年高二上学期期中数学试题(已下线)复习参考题 1人教A版(2019)选择性必修第一册课本习题第一章复习参考题河南省许昌市建安区第一高级中学2023-2024学年高二上学期10月月考数学试题四川省眉山市青神县青神中学校2023-2024学年高二上学期期中数学试题广东省广州市第六十五中学2023-2024学年高二上学期10月学情检测数学试题