解题方法
1 . 在矩形
中,
,
,在
上取一点M,在
上取一点P,使得
,
,过M点作
交
于N点,若
上存在一动点E,
上存在一动点F,使得
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecbb2dce15f3d0fe839688575d2a8ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/793f22101b6f49e98e4e87def08a0585.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cc9f041724e7fa6b08c717de02fc9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ae72eaeab4905d85253b9702d67456.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52640b15c662c870f8e499db08e1f799.png)
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6卷引用:辽宁省鞍山市台安县高级中学2022-2023学年高一下学期期末数学试题
辽宁省鞍山市台安县高级中学2022-2023学年高一下学期期末数学试题(已下线)专题05向量数量积期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)(已下线)期末测试卷01-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)第6章 平面向量及其应用 单元综合检测(难点)-《重难点题型·高分突破》(人教A版2019必修第二册)(已下线)第六章 平面向量及其应用 单元复习提升(1)-单元速记·巧练(人教A版2019必修第二册)(已下线)高一下学期期末复习填空题压轴题二十三大题型专练(1)-举一反三系列(人教A版2019必修第二册)
2 . 过
的直线与
交于
,
两点,直线
、
与
分别交于
、
.
(1)证明:
中点在
轴上;
(2)若
、
、
、
四点共圆,求
所有可能取值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8e32f16d75ccb62a04970f861827fca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c02130f82b629fab2c361dec15d41f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
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3 . 设非零向量
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c367ebf81da8ce860b8d4db598ce3b0.png)
,并定义![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de1a1abedbffcec3416ebfbba00c22b.png)
(1)若
,求
;
(2)写出![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ee7554e993fa6d1035ea7da1621b6f.png)
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/48b45cac4b26830e829a80640bf01673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c367ebf81da8ce860b8d4db598ce3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4776b8be0546414c6a82e0f7c21315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8de1a1abedbffcec3416ebfbba00c22b.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69cf5eb74f6f3b69186a665b06696d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9abc628cb2ec8b1250ac0e86a034611.png)
(2)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ee7554e993fa6d1035ea7da1621b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4776b8be0546414c6a82e0f7c21315.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fffedfb01c0a6802e19c44067252fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac41950e0db22f2216407b7e3999b51d.png)
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3卷引用:北京市丰台区2022-2023学年高一下学期期末考试数学试卷
北京市丰台区2022-2023学年高一下学期期末考试数学试卷(已下线)专题07 向量应用-《重难点题型·高分突破》(苏教版2019必修第二册)【北京专用】专题06平面向量(第二部分)-高一下学期名校期末好题汇编
名校
4 . 如图,已知
为平行四边形.
,
,
,求
及
的值;
(2)记平行四边形
的面积为
,设
,
,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a8ffec55dc1c43b460a8fef3a468d6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7872abd162e356132bb371fc581d818c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2b0246acc9bed97eef80edc52bcb37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a10f2c4a2a9c9cb4047f9f27cff1d7a.png)
(2)记平行四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1018d072c74bd0f5f013002751e16668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f021b99eb4724a997686d8ab1585382b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187d580a038d49b541c40a7e56b60c17.png)
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4卷引用:上海市黄浦区2022-2023学年高一下学期期末数学试题
上海市黄浦区2022-2023学年高一下学期期末数学试题(已下线)专题02 平面向量-《期末真题分类汇编》(上海专用)(已下线)专题05向量数量积期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)江苏省无锡市辅仁高级中学2023-2024学年高一下学期3月月考数学试卷
名校
解题方法
5 . 如图,四边形ABCD是边长为1的正方形,M,N分别是AB,AD边上的动点,下列命题中正确的有( )
A.若![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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6 . 下列说法正确的有( )
A.在![]() ![]() ![]() |
B.已知O为![]() ![]() ![]() ![]() |
C.已知非零向量![]() ![]() ![]() ![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() ![]() ![]() |
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名校
7 . 设平面向量
、
的夹角为
,
.已知
,
,
.
(1)求
的解析式;
(2)若
﹐证明:不等式
在
上恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/956879af388928628970155bdb5c2737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f8e69e4abd4e261077ed177c25ff74d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e074c209d628251349ecb15d76dfaa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafdd5eff594c3ac6bc585b05c644fe5.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31bcd4e186c9b564603e00e4dfd0e8dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe58c11b71e0ce7e6263b8112aa6140c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51742bc5df0b18cd3a6ca5abfb373bcc.png)
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3卷引用:四川省达州市2022-2023学年高一下学期期末数学试题
名校
8 . 如图,D是等边
内的动点,四边形
是平行四边形,
.当
取得最大值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e5e815fc2bbf03d424b52fa920dd0e.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebb49c1fd097c5aafc0c9080449f5fc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d439e428bc3bf8778c274dd683f4fde9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85c758dc575f8ab30df1a75f50e236a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a704469569b68ee11ab166dba3f686f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e5e815fc2bbf03d424b52fa920dd0e.png)
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四川省达州市2022-2023学年高一下学期期末数学试题上海市杨浦高级中学2023-2024学年高三上学期11月期中考试数学试卷(已下线)高一下学期期末复习填空题压轴题二十三大题型专练(1)-举一反三系列(人教A版2019必修第二册)
名校
解题方法
9 . 若点P为
所在平面内一点,且
,则点P叫做
的费马点.当三角形的最大角小于
时,可以证明费马点就是“到三角形的三个顶点的距离之和最小的点”,即
最小.已知点O是边长为2的正
的费马点,D为BC的中点,E为BO的中点,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1eab88a16df610f20dd46a44ba098d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ed53a398b1d6b7b4abbb43a9abcf1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c2372bef75fa2ba16e360b552fcf6cd.png)
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7卷引用:上海市华东师范大学第三附属中学2022-2023学年高一下学期期末数学试题
上海市华东师范大学第三附属中学2022-2023学年高一下学期期末数学试题辽宁省辽东区域教育科研共同体2022-2023学年高一下学期期中考试数学试题(已下线)第五篇 向量与几何 专题15 几何最值(费马点、布洛卡点等) 微点3 费马点、布洛卡点综合训练(已下线)8.2 向量的数量积-同步精品课堂(沪教版2020必修第二册)(已下线)专题01 平面向量压轴题(1)-【常考压轴题】(已下线)6.3.5 平面向量数量积的坐标表示——课后作业(提升版)广西南宁市第二中学2023-2024学年高一下学期5月月考数学试卷
10 . 已知向量
,
.设函数
,
.
(1)求函数
的解析式及其单调增区间;
(2)设
,若方程
在
上有两个不同的解
,求实数
的取值范围,并求
的值.
(3)若将
的图像上的所有点向左平移
个单位,再把所得图像上所有点的横坐标伸长为原来的2倍(纵坐标不变),得到函数
的图像.当
(其中
)时,记函数
的最大值与最小值分别为
与
,设
,求函数
的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e799f96093d8bfb6b5a6709ec6c4f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/946b48a52deb8046aa914743976d585d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19eec7b3f71103529d3e40a5fa885663.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24a57996290794e082b21d8f1dfc322a.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e101a51a158ada412cb00e8eccdcaf90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5226dd4e2d35264cf06db4af3b103a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ac075691407fc7a2eb3fcd3dc372d2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd8ca3aa2d1ba52e82613d0d65d800e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0862ffea88e467274cadae1d43aaae.png)
(3)若将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af9955b5aebb73cd84447e8541f901ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4091db0afc745453052bf2cdb2b6b27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa340e78e904cbfad040973ea75f3c0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb7df298a9364b36e079a61caec815c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97375cc323000d47f4809130084d0794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ab787a669e0df3c59b7251ea61ebee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a3e257ee2da131c8886346192dcd48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae4b8114fcc770a8512cf03da137ca4e.png)
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2023-03-26更新
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2卷引用:江西省抚州市资溪县第一中学2022-2023学年高一下学期7月期末考试数学试题