1 . 如图,在
中,
,
,F是AC的中点,则下列说正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72c4340dcffb0783d118a587e5352a2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ad4c0ba3a6750537789844d0ec419d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/16/5295c842-b847-40a2-aeeb-82ea41155c60.png?resizew=198)
A.若![]() ![]() |
B.若E是线段AB的中点,BF与CE相交于点Q,则![]() |
C.若E是线段AB上一动点,则![]() |
D.若点P在线段AC上,则![]() ![]() |
您最近一年使用:0次
名校
解题方法
2 . 如图,已知
是边长为1的正
的外心,
为
边上的
等分点,
为
边上的
等分点,
为
边上的
等分点.
时,求
的值;
(2)当
时.
①求
的值(用含
,
的式子表示);
②若
,分别求集合
中最大元素与最小元素的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db4fe79b98486f0d4556f37d64d74f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6faaeb653a3fc73570c131dc8a81c38d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba2ed83f255ca4c4037358d06c2fc0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0876215b2fd463d151523cd3c6b447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6ea0392d4bd0374c8a2b12a355e4655.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18627eab55012586f5894d21a11f17f5.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac3649308b528fd56545ba102dc42d5.png)
①求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0caf7b43a7461be3e697613fe2ca2112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7600d2cfbdc6146db96cc545706004f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caababdb90e1cac74532c256c4c42139.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2023-07-04更新
|
946次组卷
|
6卷引用:上海市上海中学2022-2023学年高一下学期期末数学试题
上海市上海中学2022-2023学年高一下学期期末数学试题(已下线)专题06 期末解答压轴题-《期末真题分类汇编》(上海专用)(已下线)上海市高一下学期期末真题必刷04-期末考点大串讲(沪教版2020必修二)(已下线)考题猜想03 平面向量-期末考点大串讲(沪教版2020必修二)湖南省常德市津市市第一中学2023-2024学年高一下学期4月月考数学试题(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)
名校
解题方法
3 . 已知
是
内一点,
.
(1)若
是
的外心,求
的余弦值;
(2)若
是
的垂心,
是
平面外一点,且
平面
,当四面体
外接球体积最小时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa70628a5a0f29d00104285fa7963064.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a351136b18bc7d3bd5122332772ab23b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf341193f76cf3a39f9d4fb33e52c82f.png)
您最近一年使用:0次
名校
解题方法
4 . 在平面直角坐标系
中,已知函数
的最小正周期为
,且直线
是其图象的一条对称轴.
(1)求函数
的解析式;
(2)将函数
的图象向右平移
个单位,再将所得的图象上每一点的纵坐标不变,横坐标伸长为原来的2倍后所得到的图象对应的函数记作
.
①若动点
在圆O上运动,P为圆O外一点,过点P作圆O的两条切线,切点分别为M,N,求
的最小值;
②已知常数
,且函数
在
内恰有2023个零点,求常数
与
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac70f13890d41164f6bed35b1eece80d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c366dcd7fdd83db8578a19499ffed0.png)
(1)求函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)将函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
①若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e4d47ac2e4af2aa07c4b1176dc97847.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8eb37a4dd75318dcbd836395e575bd.png)
②已知常数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60668f45298a37786757abc6a9f78897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89974ac23c340405eeace818ad30cb01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ee89c399a3c7e54f745b0f0a2e90e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
您最近一年使用:0次
名校
解题方法
5 . 已知
中,
,
,
是线段
上的两点,满足
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3a059203f65774fd8f321faa9e8041.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/6703a78d8d161ec1b7bcd5dcfe45b22e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8149e6cd3d2f2304af7a8527002a6bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1cf680b83dd7afbca098d80d370ca2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb7025bdeee3a087a9c25f0dc564f36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16ca90e8a784f990c4097eec9219908d.png)
您最近一年使用:0次
2023-04-14更新
|
983次组卷
|
4卷引用:广东省阳江市2022-2023学年高二下学期期末数学试题
解题方法
6 . 若单位向量
满足
,向量
满足
,则
( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2dff77b482a9f7ceb893bfef29539a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd91eb66f58980cb69a9bf755462000a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9843f19ca2338f7f126ca8c5eb447b55.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-02-14更新
|
2866次组卷
|
4卷引用:浙江省宁波市慈溪市2022-2023学年高三上学期期末数学试题
浙江省宁波市慈溪市2022-2023学年高三上学期期末数学试题(已下线)专题03 平面向量的综合应用(1)-期中期末考点大串讲安徽省卓越县中联盟2024届高三上学期第三次质量检测数学试题(已下线)平面向量的应用
名校
解题方法
7 . 我们把一系列向量
,
,
按次序排成一列,称之为向量列,记作
.已知向量列
满足:
,
(
,
)
(1)求数列
的通项公式:
(2)设
,问数列
中是否存在最小项?若存在,求出最小项;若不存在,请说明理由.
(3)设
(
)表示向量
与
间的夹角,
为
与
轴正方向的夹角,若
,若存在正整数
,使得不等式
成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a47bdc03f0ced8245c526c81593363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4f79c1b52b08b72cf398a8e62e5fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a4f79c1b52b08b72cf398a8e62e5fc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c22453d6e8bba93f0efb02a79344c42e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1eedb01adf41122a75af856f9bfd20d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e167b43045b3297248e334c41c621b8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4613271f782a90ab580131d09d03d1.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3ca98775fedd51d48b847a3e52d6c7.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02c3b72c21e23e30ebcb10966fb148a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ffa8be5a02790c6161c56b8e90db64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d624036bd9f528841f32ad7dbaba229.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4a47bdc03f0ced8245c526c81593363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d344174267f996c7cefecfd6985d380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fe10104403f4d1eeb171b96589cf9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4cca4a0d567628bc9fcd8923eeaa212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
8 . 在
中,
,D为BC上一点,E为AD上一点,F为EC上一点,且
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02cd4fd97a975f810756a0b1324dcc93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cabcef1cee1213140371c499339864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f46f19939f38833f9152942f8241b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb2a9124572cbb2748323c726c456a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d18e0f2bd21f30068b79b29a1a19f0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96724b211bf3e56d588bd430aa3f2894.png)
您最近一年使用:0次
2022-10-05更新
|
1172次组卷
|
4卷引用:吉林省长春市第六中学2022-2023学年高三上学期期末数学试题
名校
解题方法
9 . 已知
是单位向量,向量
满足
,且
,其中
,且
.则下列结论中,正确结论的序号是___________ .
①
;
②
;
③存在x,y,使得
;
④当
取最小值时,
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56eda4bb8604c18d0016a4377d05435a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd37f7f1058b31cd36e871ea80e6edee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4540e84bfb9ff9bb9f95d4d51dc99024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1157bfeb62efbb32bf37986e1b5affb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ab4b75fa22deba7fcbcdcb31dd45b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5558c083d34cbb0a58d3ce1dc6f5778e.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb9930c5b264d8e8602a6267d1015b0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6315a65f0d41676603e4e15d3da0145.png)
③存在x,y,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a651125429f3ecc99794c427c354377.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4243432eb9da670db29b50c16109f9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979f456da73404e2f82c94a0170248ac.png)
您最近一年使用:0次
2022-07-08更新
|
1920次组卷
|
4卷引用:北京市朝阳区2021-2022学年高一下学期期末质量检测数学试题
北京市朝阳区2021-2022学年高一下学期期末质量检测数学试题(已下线)第六章 平面向量及其应用(基础、典型、易错、压轴)分类专项训练(3)湖南省衡阳市第八中学2024届高三上学期第五次月考数学试题(已下线)专题01平面向量线性、数量积运算4种常考题型归类-《期末真题分类汇编》(北京专用)
名校
解题方法
10 . 在矩形
中,
,
,
,
是平面
内的动点,且
,若
,则
的最小值为____ .
![](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/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d582d3e7ec013a1b409810ed38633d7c.png)
![](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/9a8c4f87043cd193f95d6ebcc1fc5f5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d61f98f7418eda31a1d7c457e3841c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/990b2fb4961eebd49a6eb62e2beef238.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/6/26/a0c2d1bc-b38f-4cd6-8830-5e9fc86a037f.png?resizew=186)
您最近一年使用:0次
2022-06-25更新
|
1576次组卷
|
5卷引用:浙江省丽水市2021-2022学年高一下学期普通高中教学质量监控(期末)数学试题
浙江省丽水市2021-2022学年高一下学期普通高中教学质量监控(期末)数学试题青海省西宁市城西区青海湟川中学2022-2023学年高三上学期12月月考文科数学B试题(已下线)专题8-1 直线与圆归类(讲+练)-3(已下线)重难点01平面向量的实际应用与新定义(2)(已下线)上海市华东师范大学第二附属中学2023-2024学年高二上学期10月月考数学试题