解题方法
1 . 在平面直角坐标系
中,已知点
,点
在第二象限,且
.
(1)若点
的横坐标为
,现将向量
绕原点
沿顺时针方向旋转
到
的位置,求点
的坐标;
(2)已知向量
与
,
的夹角分别为
,
,且
,
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e15dcec65e64874dc2672de217573e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74506fc084f102994675ca1ef895622a.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91174b2336306191ba275a87864172b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c074eecd00175381ab99a16ab069cbfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a0c6e30ec069f3dddbab37e292bf3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e06ca53803f042a5eca99f56a70f05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
您最近一年使用:0次
2023-08-02更新
|
439次组卷
|
5卷引用:第六章 平面向量与复数 综合测试B(提升卷)
(已下线)第六章 平面向量与复数 综合测试B(提升卷)山东省威海市2022-2023学年高一下学期期末数学试题(已下线)第07讲 6.3.2-6.3.4平面向量数乘运算的坐标表示(2)-【帮课堂】(人教A版2019必修第二册)(已下线)第一次月考解答题压轴题十六大题型专练(1)-举一反三系列(人教A版2019必修第二册)【人教A版(2019)】专题03三角函数(第三部分)-高一下学期名校期末好题汇编
2023高三·全国·专题练习
2 . 如图,
为
所在平面上一点,过
作直线
,由平面向量基本定理知:存在
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d620f242099d9e5e3225115c80d9bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dcbca3478eae63853d2aab5332e2e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e06ca53803f042a5eca99f56a70f05e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/16/97d9378e-e1c8-46e2-981a-4c91a532faeb.png?resizew=170)
您最近一年使用:0次
名校
解题方法
3 . 如图,点
分别是正方形
的边
、
上两点,
,
,记点
为
的外心.
,
,
,求
的值;
(2)若
,求
的取值范围;
(3)若
,若
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff3507599c740c4c7f486cd19ee39fb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4fca387f03e4b2fdb0c64a79b6a0605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cebec80e8dcce975425a46c728c26b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd3ede869e508a8c8bda34a16782f863.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42206793edde00d2d43cd07adf78366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5604d3e156df3e7ccca0ccec9c9d45.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72bf0fce80daad394f2a9d013829c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e91eeb57e4fc87e26efb7d371f6f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1655e1de5516f9764871df59c0469dd.png)
您最近一年使用:0次
2023-04-21更新
|
1411次组卷
|
9卷引用:FHgkyldyjsx06
(已下线)FHgkyldyjsx06浙江省浙北G2联盟2022-2023学年高一下学期4月期中联考数学试题江西省宜春市高安市灰埠中学2022-2023学年高一下学期5月期中考试数学试题(已下线)第6章 平面向量初步-【优化数学】单元测试能力卷(人教B版2019)(已下线)结业测试卷(范围:第六、七、八章)(提高篇)-【寒假预科讲义】(人教A版2019必修第二册)(已下线)专题6.12 平面向量及其应用全章综合测试卷(提高篇)-举一反三系列(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)江苏省苏州市张家港市沙洲中学2023-2024学年高一下学期3月阶段性测试数学试题(已下线)第一次月考解答题压轴题十六大题型专练(1)-举一反三系列(人教A版2019必修第二册)
名校
解题方法
4 . 已知M,P,N是平面上不同的三点,点A是此平面上任意一点,则“M,P,N三点共线”的充要条件是“存在实数
,使得
”.此结论往往称为向量的爪子模型.
(1)给出这个结论的证明;
(2)在
的边
、
上分别取点E、F,使
,
,连结
、
交于点G.设
,
.利用上述结论,求出用
、
表示向量
的表达式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ba27da4302c066fa4cf802ef5829b90.png)
(1)给出这个结论的证明;
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.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/12936b86da4c79d7705b233baa336ecf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0b80c5888abb4ac33ae0ec9d834a9f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d82dcb8d9047d6769989282c53b08e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5691149a894127b6dccf09cb340d4247.png)
![](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/4db1ab520617e340ca2d38b104bd3598.png)
您最近一年使用:0次
5 . 已知函数
为二次函数,点
分别为函数
图像上的三点,点
为
图像上的任一点.
(1)求
的最小值;
(2)若
是以
为直径的圆的一条直径,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42d4d66091ca581dd23b2e9c4f12405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb788ae88e457017bb81120b6a2e5ee.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6356488b921e900ad8f0448d20e918e6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fd3a87ff523729402741d91ec701f6.png)
您最近一年使用:0次
2022-10-10更新
|
138次组卷
|
2卷引用:河南省名校联考2022-2023学年高三一轮复习诊断考试(一)理科数学试题
解题方法
6 . 已知平行四边形
中,
,
,AE和BF交于点P.
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987010527412224/2988279555710976/STEM/9badeac5-c79e-441a-aa96-5b4da5d385a9.png?resizew=196)
(1)试用
,
表示向量
.
(2)若
的面积为
,
的面积为
,求
的值.
(3)若
,
,求
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70b9197520d3da41e2e01480f580e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/048f7048ab21fd6a752f3f64d9a4db30.png)
![](https://img.xkw.com/dksih/QBM/2022/5/25/2987010527412224/2988279555710976/STEM/9badeac5-c79e-441a-aa96-5b4da5d385a9.png?resizew=196)
(1)试用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fe2d802f2b37e7db198c5a3c1df9a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228f4ddbb8959f904d71259be7c6ab36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1395fa3420959a18d91b324adc622116.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3cd61d00f89e68ccca2cac5c937783.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceff3844281849df3e37a2e56e110549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034d174a0dfdfb1d66f1b62b6eef445c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923e40c9e7682a0c2d0006b6398c1e5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bac5b9c067002bc06fb400d6c4f3512.png)
您最近一年使用:0次
名校
7 . 已知点D,P在锐角
所在的平面内,且满足
,
.
(1)若
,求实数
,
的值;
(2)已知
,其中
为
的面积.
①求证:
;
②求
的最小值,并求此时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8488ec91652ad560475f6d45c8e20b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b59cbb44ed46540f65fa7efb5e313144.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57766a96c4b7e39bc224fa5917c6be22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8ec4fc7447298cbd6f51ee9977b005f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2aa7ba35117b8963954c65934c8f8c.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39344ad1a4a45a1023de6b5bdda76546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a24a8f5e8fb89381f8add6549170345.png)
您最近一年使用:0次
名校
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
|
434次组卷
|
3卷引用:专题13 平面向量(练习)-2
名校
9 . 如图,圆O是△ABC的外接圆,D是圆外一点,BD与圆O相切于点B,
,证明:A,O,C三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dc5270c3aa0965eee31bd3dd779e00b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/cb838256-b5a9-487d-a834-85940d85fd56.png?resizew=150)
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)
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