名校
1 . 在△ABC中,
,F是AC的中点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3906093705a041d34a663bde830d40da.png)
A.若![]() ![]() |
B.若E是AB的中点,BF与CE相交于点Q,则![]() |
C.若点P在线段AC上,则![]() ![]() |
D.若E是线段AB上一动点,则![]() |
您最近一年使用:0次
2022-07-18更新
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459次组卷
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2卷引用:福建省莆田市2021-2022学年高一下学期期末数学试题
名校
2 . 关于平面向量,下列说法正确的是( )
A.若![]() ![]() ![]() |
B.已知![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
2021-08-07更新
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687次组卷
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2卷引用:山东省临沂第一中学2021-2022学年高一下学期6月月考数学试题
名校
解题方法
3 . 在
中,点D在边BC上,且
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ec8bc62f9491231ad5b8527dbd07ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ace1f0505dac8a8ea7bca12dc94eb41.png)
,记
中点分别为
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d78524f98b01fa1dadfd277939665b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ec8bc62f9491231ad5b8527dbd07ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ace1f0505dac8a8ea7bca12dc94eb41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158a47ad74fdd9a44e9fc0403d6381b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dab67d1b4a722079cd03b7b0a0e89ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3767efa8adfb71001ad39df9560cbf6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db6f1b16c63ef1269d4f5b366e7b3b94.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-10-27更新
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396次组卷
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2卷引用:江苏省南京市、盐城市部分学校2022-2023学年高三上学期10月第一次联合调研数学试题
名校
解题方法
4 . 如图,在平行四边形ABCD中,BD,AC相交于点O,设向量
,
.
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986258300076032/2995511888650240/STEM/9de97c5c-711a-4ef4-bcac-847b592df251.png?resizew=256)
(1)若
,
,
,求证:
;
(2)若点P是平行四边形ABCD所在平面内一点,且满足
,求△ACP与△ACD的面积比;
(3)若
,
,点E,F分别在边AD,CD上,
,
,且
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7a93a1399ff7a2bde342652479241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3b54aa2b7f9adf409f0ce8e00615432.png)
![](https://img.xkw.com/dksih/QBM/2022/5/24/2986258300076032/2995511888650240/STEM/9de97c5c-711a-4ef4-bcac-847b592df251.png?resizew=256)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82d16399c8b393539c774d06f410cbe.png)
(2)若点P是平行四边形ABCD所在平面内一点,且满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfcc49ef13196d82c91f1291b436616a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27db558e8db4c957654c8e5cecd2d2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55881285c3bea9e25144254cf2037540.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5da346525c48808ae3dca8a05e4408b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec945b565730ef11fe66334927dede1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bc29cb1d0b8ca9c4d6286c892952653.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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解题方法
5 . 在平面直角坐标系
中,
是直线
与曲线
在第一象限的交点,
是直线
上的一点,且满足
.
为曲线
上动点,当
取最小值时,
的横坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa2fa89a25879322c4cb884763b79104.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4f415ebe14b7a5b4fbc3f86393d887.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b7937ef6b4a2b4d25dc8bbd6c50ba25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9155e905785b48d3a58fabd03e2ed04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
6 . 如图,已知点
是边长为1的等边
内一点,满足
,过点
的直线
分别交
,
于点
,
.设
,
,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760355507085312/2762005288312832/STEM/e8e74121-cd2e-4fad-b0c5-ff82aad8ae16.png?resizew=264)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c41af21f3c86faeb4b18e6ba7abf67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.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/4f0d53573554894dbe3b31027d7cdfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86c9ca024d66f87e779fee3922c3b37b.png)
![](https://img.xkw.com/dksih/QBM/2021/7/9/2760355507085312/2762005288312832/STEM/e8e74121-cd2e-4fad-b0c5-ff82aad8ae16.png?resizew=264)
A.![]() | B.点![]() ![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2021-07-11更新
|
473次组卷
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4卷引用:广东省广州市第四十一中学2021-2022学年高一下学期4月月考数学试题
广东省广州市第四十一中学2021-2022学年高一下学期4月月考数学试题(已下线)专题02 平面向量的相关计算(中档题)-【重难点突破】2021-2022学年高一数学常考题专练(人教A版2019必修第二册)山东省潍坊市2020-2021学年高一下学期期末数学试题湖北省黄冈市蕲春县2021-2022学年高二上学期期中数学试题
21-22高一下·上海浦东新·阶段练习
名校
7 . (1)已知
为
外接圆的圆心,若
,
,则
是否为定值?若是,求出这个值;若不是,请说明理由;
(2)若点D为边BC上一点,点E为边AC中点,AD与BE交于点P,且
.若
(x、
),求x、y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/f371c0b1d573c06516ab1904d95ee49f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54c556458d8075aa2d133615725f8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f56f3ad7839112bd580857479d253883.png)
(2)若点D为边BC上一点,点E为边AC中点,AD与BE交于点P,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b10bc9e1a36293cca8dc7c5297b17736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74f92aef16f5f17f7613e92f34c38e82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cccdff49c3efe6e7a7dbbf69db9319.png)
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8 . 如图,在四边形
中,
为对角线
与
中点连线
的中点,
为平面上任意给定的一点.
![](https://img.xkw.com/dksih/QBM/2021/6/18/2745403371003904/2768546705989632/STEM/46cde7beb3864628b0df3a3de5e77c2e.png?resizew=93)
(1)求证:
;
(2)若
,
,
,
,点
在直线
上运动,当
在什么位置时,
取到最小值?
(3)在(2)的条件下,过
的直线分别交线段
、
于点
、
(不含端点),若
,
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/2021/6/18/2745403371003904/2768546705989632/STEM/46cde7beb3864628b0df3a3de5e77c2e.png?resizew=93)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5632cbd5252f07934ecdb6e6951246f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4a0816f8db1e1cad53f05b8dc1837ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed8128329f973dff60d13e4039957b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7652bbae10722db2cf0458d9da4a54c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f82432e6351f381c0008e5bc6b545f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc4a9a1594591b27b24998ea3f5a2e5.png)
(3)在(2)的条件下,过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3834d7ec7531f3c3c0ce9b286f7a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da25790e5a2cc740b8a5ef8809dab3a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/660018ccbfd4abf386c30cad0f9ea8eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27e62ba44cbfec6823ebc1f0c7457fb.png)
您最近一年使用:0次
2021-07-20更新
|
432次组卷
|
3卷引用:上海市上海师范大学附属中学闵行分校2021-2022学年高一下学期期末数学试题
9 . 已知O,A,B为平面上三点,若
,
,动点P和实数
,
满足
,
,
,则动点P轨迹的测度是__________ .(注:当动点的轨迹是曲线时,其测度指其长度;当动点的轨迹是平面区域时,其测度指该区域面积.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbabeab7e7d0e4bcd21a188362b5b9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22905409f038387f0e954a47384b60a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59bca4c0ab83a3ca3b0ebf03281be74f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88b381aeca13cc17c8217a6db4d2c2ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a22570173ffa333a304977f3ee7df28.png)
您最近一年使用:0次
名校
10 . 有下列命题:
①已知
是平面内两个非零向量,则平面内任一向量
都可表示为
,其中
;
②对平面内任意四边形
,点
分别为
的中点,则
;
③已知
与
夹角为
,且
,则
的最小值为
;
④
是
的充分条件.
其中正确的是_______ (写出所有正确命题的编号).
①已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ccba3b87a8a48ac3dd5f72d00bdb1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a46718baf2e8edbecb5ad89dbef500b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9856d7365df4143ae465b3cfac5fb43b.png)
②对平面内任意四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b565db8efd442ebd51f54115b4e3197.png)
③已知
![](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/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c73dcfe1b9e26ec743d0a6caeed65f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3357a4707fbe4ef93661a64e88881d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9563540452712a60d70f76cf22a868c9.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9c13327875f7ecbfe021841d6f681a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/912b685ef77dc22f30ae53611b4d1452.png)
其中正确的是
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