名校
解题方法
1 . 知正方体
中,
、
分别为对角线
、
上的点,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c525e70f9f3d864840080804ae96819d.png)
平面
;
(2)若
是
上的点,
的值为多少时,能使平面
平面
?请给出证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c525e70f9f3d864840080804ae96819d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72221ee5b504d596ff799c0b356aa0ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4da530384dd04ac90a025385e8b3c2f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943d6e170279d007a4c943f684b1c3c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8fd9020ac4827433593c1e3d503a30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4da530384dd04ac90a025385e8b3c2f.png)
您最近一年使用:0次
名校
解题方法
2 . 如图,已知
是圆
的直径,
平面
,
是
的中点,
.
平面
;
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1afe4a56c1bd9fbe4850410e4133bd24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b1e86a4f4bd9250b5b0a752b838779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,已知
是平行四边形
所在平面外一点,
、
分别是
、
的三等分点(
靠近
,
靠近
);
平面
.
(2)在
上确定一点
,使平面
平面
,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28a07491270be75a3697538bec706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
您最近一年使用:0次
名校
4 . 证明:
(1)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8fffe92548da698866a9888e57d472.png)
(2)![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c85bf2963df20faabb0e5b2f512e55.png)
(3)已知
,
,求证
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8fffe92548da698866a9888e57d472.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c85bf2963df20faabb0e5b2f512e55.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c0975b825228b2a91799eee6894987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57802c9ef29020d70c31d10d8c19125f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca26c7f4cf6a970f1f7c400ac2fc53ac.png)
您最近一年使用:0次
5 .
个有次序的实数
所组成的有序数组
称为一个
维向量,其中
称为该向量的第
个分量.特别地,对一个
维向量
,若
,
,称
为
维信号向量.设
,
,则
和
的内积定义为
,且
.
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在14个两两垂直的14维信号向量;
(3)已知
个两两垂直的2024维信号向量
满足它们的前
个分量都是相同的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27bb33ccdad573e2b2b0e7facbcca07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6d038f2967ee70acc7777c32c8b43c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9925b25d5708cbd87f69cca1b5c66c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c05b9832b09731a574d4a4adf7448de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143f87bed8eee1f43d3e67be747b7d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcadd9ce3631b6e230fe7b21a0719c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e0d46fb5c7c978e4fe9c23f33ba151.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37564ec4e9e92485f1769e8ffaac31d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/143f87bed8eee1f43d3e67be747b7d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/777dac26504cae699de348ec1df9dc4a.png)
![](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/8346ea7024dd0c905cc4c80cb16dc6a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c7c807358869b70becd16ca80e1714.png)
(1)直接写出4个两两垂直的4维信号向量;
(2)证明:不存在14个两两垂直的14维信号向量;
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb9cae65660b220cc622b87ed9eea092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf2182d0dad848ccc76944d976befbf2.png)
您最近一年使用:0次
2024-02-23更新
|
690次组卷
|
6卷引用:高一数学下学期期中模拟卷(新题型)-同步题型分类归纳讲与练(人教A版2019必修第二册)
(已下线)高一数学下学期期中模拟卷(新题型)-同步题型分类归纳讲与练(人教A版2019必修第二册)(已下线)模块一 专题3 平面向量的应用(B)广东韶关实验中学2023-2024学年高一下学期3月月考数学试题(已下线)模块一专题3 《平面向量的应用》B提升卷(苏教版)(已下线)模块三专题4大题分类练(专题3 平面向量数量积)【高一下人教B版】湖北省武汉市华中师大第一附中2023-2024学年高二下学期数学独立作业(一)
6 . 如图,已知四棱锥
中,底面
为平行四边形,点
分别在
上.
,求证:平面
平面
;
(2)若点
满足
,则点
满足什么条件时,
平面
?并证明你的结论.
![](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/8a5f302c1c2f7e1b46cad05594ed672e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bba2613c7a68fbe3478e4cf3dccf8fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480eb43bbb9a6e3ef0c7cc491e860b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b28a07491270be75a3697538bec706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bc5e89527a4e52c83ba66b388c3542.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/982d01f052709b72afeaf1015fc7acc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7ffa7d57cb72ca3468f448e70b52af.png)
您最近一年使用:0次
解题方法
7 . 已知幂的基本不等式:当
,
时,
.请利用此基本不等式解决下列相关问题:
(1)当
,
时,求
的取值范围;
(2)当
,
时,求证:
;
(3)利用(2)证明对数函数的单调性:当
时,对数函数
在
上是严格增函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db5e0630a1632f6368fb824ebfdead0d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7326ea56be82bd616fec7e6aa3c884c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1419108104429f6df5d5352a05211e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca16bee4a8ecee60c31f9aaac02539b0.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27eb687fdf1568ab06ce8119845823c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c92098b3da769963a2320cf1d8dad00a.png)
(3)利用(2)证明对数函数的单调性:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d33da711e50e96568facb18cef27165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82869dad28f771d088772a2c2b08b187.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d562dc22dfb3b81d0c3f88b54d063c2f.png)
您最近一年使用:0次
名校
8 . 设非零向量
,并定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b559f7fde1a5c323bed55d47d4384a.png)
(1)若
,求
;
(2)写出
之间的等量关系,并证明;
(3)若
,求证:集合
是有限集.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7294acbd5cfb00d84de7ddd4666b80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b559f7fde1a5c323bed55d47d4384a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffebbdbafed89a76874f0864780c0434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb8c29dc5e8135c50ab73b1e7b029527.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e34127cc34640277362872bf812ca9.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fffedfb01c0a6802e19c44067252fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf0984fd006a9ece396aba8f031a8e9.png)
您最近一年使用:0次
2024-05-09更新
|
119次组卷
|
4卷引用:【高一模块三】类型1 新定义新情境类型专练
(已下线)【高一模块三】类型1 新定义新情境类型专练福建省泉州第五中学2023-2024学年高一下学期期中考试数学试题福建省福州市闽侯县第一中学2023-2024学年高一下学期第二次月考(5月)数学试题(已下线)专题03 平面向量的数量积常考题型归类-期末考点大串讲(人教B版2019必修第三册)
2024高二·全国·专题练习
解题方法
9 . 如图,在四棱锥
中,底面
是
且边长为
的菱形,侧面
为正三角形,且其所在平面垂直于底面
.
;
(2)若
为
边的中点,则能否在棱上找到一点
,使平面
平面
?并证明你的结论.
![](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/c6e0b64d25ddd18454f88e40c45d7d8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdfa54114f04a75b8c96165b3718ed7f.png)
(2)若
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f6dd051db98c531f9ef18cdfd793f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
10 . 固定项链的两端,在重力的作用下项链所形成的曲线是悬链线.1691年,莱布尼茨等得出“悬链线”方程
,其中
为参数.当
时,就是双曲余弦函数
,类似地我们可以定义双曲正弦函数
.它们与正、余弦函数有许多类似的性质.
(1)类比正弦函数的二倍角公式,请写出双曲正弦函数的一个正确的结论:
_____________.(只写出即可,不要求证明);
(2)
,不等式
恒成立,求实数
的取值范围;
(3)若
,试比较
与
的大小关系,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852665ec9c3a65b758898059361f11a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4580cc037c0c760c728cdbb74a8154c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a7c1d3681898e25187a896aeb0c8c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0718c04bdf70989bcc90b902671a692.png)
(1)类比正弦函数的二倍角公式,请写出双曲正弦函数的一个正确的结论:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d8fe1e65b09697538d4dee0746846f4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fe9f3099ed9429dc5b4e38a350e524a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343e7c30c2a5d166819b28e23fad2203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/563f464c94feac28033f6f3a271fbe8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2cebaab3423dfb2f2c944dfc43df8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb966b7b2dd6581640bcee2d97dacf77.png)
您最近一年使用:0次
2024-01-27更新
|
946次组卷
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9卷引用:第八章:向量的数量积与三角恒等变换章末重点题型复习(2)-同步精品课堂(人教B版2019必修第三册)
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