21-22高一·湖南·课后作业
解题方法
1 . 证明不等式:
(1)若
,
,
,
都是正数,求证:
;
(2)若
,
,
是非负实数,则
;
(3)若
,
是非负实数,则
;
(4)若
,
,则
.
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e7387a3fbab6508695365955f55258.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2d92a6b95fdfdedb405447340293bdc.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727ff3ac24b506706045956c16336f94.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19339e3904e9541ff26b30ae5f1242b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f58b9bc974b789928f6490acb43fb3.png)
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2 . 图中四边形ABCD,DCEF,FEGH都是正方形,用复数方法证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6e7b446e3329dfe2894751f93cf0c1.png)
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21-22高二·江苏·课后作业
解题方法
3 . 已知数列
和
是两个无穷等差数列,公差分别为
和
,求证:数列
是等差数列,并求它的公差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5edf900c810371fb21297c15f86d8743.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b31ac1def558351e2e3ed1235c570530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5344eadd4711db34e3f935aedd5fb270.png)
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21-22高二·江苏·课后作业
4 . 已知
,点
,
,直线
.求证:点P到直线l的距离等于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a449474e7cf366add572ca32014a23e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f6d06b9a4d3a891ea7c986b1ab4e925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c75f0d9463771a3aba1865a9d9d398aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ac654a052f98d1ccb7fede1f122cec3.png)
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21-22高一·湖南·课后作业
解题方法
5 . 用向量运算刻画三角形的重心.
(1)已知
,求一点G满足
.
(2)求证:满足条件
的点G是
的重心.
(提示:说明点G同时在
的三条中线上.)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c41af21f3c86faeb4b18e6ba7abf67.png)
(2)求证:满足条件
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c41af21f3c86faeb4b18e6ba7abf67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(提示:说明点G同时在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2022-02-22更新
|
836次组卷
|
8卷引用:专题03 向量的数乘(2)-《重难点题型·高分突破》(苏教版2019必修第二册)
(已下线)专题03 向量的数乘(2)-《重难点题型·高分突破》(苏教版2019必修第二册)(已下线)1.3 向量的数乘(已下线)专题02 平面向量的运算-2021-2022学年高一《新题速递·数学》(人教A版2019)(已下线)6.2.3向量的数乘运算(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)(已下线)6.2.3向量的数乘运算(精练)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)湘教版(2019)必修第二册课本习题 习题1.3(已下线)第02讲 平面向量的运算-【寒假预科讲义】(人教A版2019必修第一册)(已下线)【高一模块四】 回归1 平面向量的课本典型例题和习题
6 . 已知空间向量
,
,
,
,若存在实数组
和
,满足
,
,且
,求证:向量
,
,
共面.
![](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/8b1bfbd2ef51eaeb6e686e27cc95638e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa7abe36a6aa866ac4d4e0ca83653cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c36e846eb9d6fbaadcb9b9b745779a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0237dc4d7381893117a3aa4784afd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ab74bb8aca5f0c69cbe968baf7eb6ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bd24e647a626899a243a3f3984f90a.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)
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2021-12-05更新
|
206次组卷
|
4卷引用:6.1空间向量及其运算
(已下线)6.1空间向量及其运算(已下线)专题一 专题1 空间向量与立体几何(1)(高二苏教)苏教版(2019) 选修第二册 名师导学 第六章 6.1.3 共面向量定理苏教版(2019)选择性必修第二册课本习题6.1 空间向量及其运算
21-22高一·湖南·课后作业
7 . 已知:
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e93622d238a10ef084d02a25e7d6e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f46c90b74747b4fbe7a10577158e998c.png)
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21-22高二·江苏·课后作业
解题方法
8 . 如图,由原点O向直线
作垂线ON,垂足为N.设
,ON与x轴正方向所成的角为
.
的方程为
;
(2)利用上面的方程推导点
到直线
的距离公式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbb6a528a39bdc4b4496605a4d3f5cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4a19b2e42c49f3ff978d1d22e7871ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19c1fbb2c0c27bd9b3bc737da0a7baa8.png)
(2)利用上面的方程推导点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc26262f7a1603369462c7c2f2197a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6b6e44dd054b54f89e7c237eb1428da.png)
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21-22高一·湖南·课后作业
9 . 如图,矩形ABCD的相邻两条边AB,BC的长度分别为1和3,点E,F是BC的三等分点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67207077ac81e66c05f8e210bcb84862.png)
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21-22高一·湖南·课后作业
10 . (1)如图,O为
的外心,H为
内一点,且
.求证:H是
的垂心,(提示:
.)
所在平面内任一点,其余条件不变,(1)中的结论还成立吗?
![](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/1ef5de81202c50e6a5f52b955af24722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d22eeb58f99ef6398386dcde4a3c3d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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