名校
1 . 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
|
481次组卷
|
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
2 . (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)
您最近一年使用:0次
名校
3 . 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
|
434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
4 . 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
解题方法
5 . 已知在
中,
,
,
,点D满足
,点E满足
,其中
.
(1)求
的值;
(2)用向量方法判断是否存在
使
,若存在,求
的值;若不存在,说明理由;
(3)令AE与CD相交于点O,若
,请用
表示实数t.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c278812c4813f6391c7993574e2f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b59ab6bf6111dda4a3d428454768b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fdd8e57562ba94e10e7f1d770826d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0d53573554894dbe3b31027d7cdfe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a779c29506937cf02995e1f2e8935f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e41211eef74318dbf464acf1a716fdd.png)
(2)用向量方法判断是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4611ceb2a28f7a7e4d24266d7f99b22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)令AE与CD相交于点O,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ecc633ba1ec1a478a170cb7864820be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
6 . 如图,已知向量
的起点相同,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8bce9bdc1f102d7640acc15aaa5200.png)
( )
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710414906130432/2785822477942784/STEM/439d743618a14bd68032c0de3a937f45.png?resizew=200)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e769105e5cb53aa51eead65603b27c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce8bce9bdc1f102d7640acc15aaa5200.png)
( )
![](https://img.xkw.com/dksih/QBM/2021/4/29/2710414906130432/2785822477942784/STEM/439d743618a14bd68032c0de3a937f45.png?resizew=200)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-08-16更新
|
365次组卷
|
2卷引用:北京理工大学附属中学2021-2022学年高一3月月考数学试题
名校
7 . 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
您最近一年使用:0次
8 . 以下说法正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/7/079483d1-2d86-491e-b32c-47585ca23d22.png?resizew=194)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/7/079483d1-2d86-491e-b32c-47585ca23d22.png?resizew=194)
A.对![]() ![]() ![]() |
B.设![]() ![]() |
C.若![]() ![]() ![]() |
D.正方体![]() ![]() ![]() |
您最近一年使用:0次
解题方法
9 . 如图,
中,
,
,
,
,
,点
,
满足
,
,
,
与
交于点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/59faf1d5-dc10-4e7c-8a2b-594709735bbd.png?resizew=178)
(1)当
时,请用
,
表示向量
,并求
的值;
(2)用
,
表示向量
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea0df817e3e2cd95b9cd8f73386834c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d6baf49925a5bcb359b542d45067c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b969c7a52b761665011ec06b5e392e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae60c09521904ab969829bf0d74edd37.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/2008b996728711d019c37519a327106e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7155ba45d20bb7292f14e7c31fd5a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/13/59faf1d5-dc10-4e7c-8a2b-594709735bbd.png?resizew=178)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3cf0f585938ede9eca890a6eb326d.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/888afd002858f23a84a8755a002bed7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90a161255d0fb0d472fdb983f64d498e.png)
(2)用
![](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/c4648d56ec5ba86c288bc22737250ba0.png)
您最近一年使用:0次
20-21高二下·浙江·期末
10 . 已知等边
的边长为2,点D是
边上的中点,点E是
边上靠近点A的三等分点.
(1)设
,请直接写出
的最小值及对应的实数
;
(2)设
与
交于点O,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995ec593baa4ef50b6d87c78380953d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40a28142ca1f7f26e09abced156daba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef3004955f86556fa23f1d3ac9b37651.png)
您最近一年使用:0次