1 . 如图在
中,
是边
的中点,
是
上靠近
的三等分点,
与
交于
点,过点
的直线与线段
,
分别交于
,
(不与端点重合).设
,
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c152a956b42568d78cae545ac3a89ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ae362301a3faf1d70ae622e45ea386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaacfaef44a654c0a1c283ef03fc0550.png)
您最近一年使用:0次
2021-08-28更新
|
257次组卷
|
3卷引用:黑龙江省西北部八校2021-2022学年高一下学期期中联考数学试题
黑龙江省西北部八校2021-2022学年高一下学期期中联考数学试题安徽省黄山市屯溪第一中学、中科大附中2020-2021学年高一下学期期中联考数学试题(已下线)江苏省南京市六校联合体考试2023-2024学年高一下学期4月期中数学试题变式题11-15
名校
解题方法
2 . 如图所示,在
中,
,
,
与
交于点
.过
点的直线
与
、
分别交于点
,
,若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1642b5e397829c6aa01dca94d0aa717.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec6db75d7769d4866644abb4e46896d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef86ffd2bf72dcfb82b82f839a35e452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9795568e7c599718a29bc80cc3405233.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f4fdd03782afd69e06cdd75fb050b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1642b5e397829c6aa01dca94d0aa717.png)
![](https://img.xkw.com/dksih/QBM/2021/5/25/2728844239937536/2763351313162240/STEM/f0a7bb6f15134dfea7b51b454deb46dc.png?resizew=185)
您最近一年使用:0次
名校
3 . 已知向量
,
,
,
,若
,则
的最小值为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc97dbad947c85e02c28dd08ddb57d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4695dd11fc436e4ce9337987d0a5f932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70facc9bc02af0867d248407bd317c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d760204a261aae858ee3e353882899.png)
您最近一年使用:0次
2021-07-10更新
|
626次组卷
|
5卷引用:黑龙江省大庆铁人中学2021-2022学年高二上学期开学考试数学试题
名校
解题方法
4 . 已知
,
夹角为120°,
,
.
与
夹角为150°,如图所示位置
,若
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
___________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0719844e0261af3b625d9673e5926.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/70e310702748855c3edccd151aae0143.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34fa8ea29001bb1f0c1e5157aff2fca5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5b3355ee9ba032587b89203adff55c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6b282bb21a9767162b6e18e15ef87c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0719844e0261af3b625d9673e5926.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/5e863d44-246c-4e2a-b057-039b6ddc544a.png?resizew=165)
您最近一年使用:0次
20-21高一下·浙江·期末
名校
解题方法
5 . 如图,在
中,
是线段
上的一点,若
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180892bd2ef1587b1982a2124080fdc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8320518d2bdba8d75cdbf327e3448e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
![](https://img.xkw.com/dksih/QBM/2021/4/21/2704443437498368/2704503205773312/STEM/036c1ed6-73aa-4a3b-b9bc-4e91a97f3500.png?resizew=257)
您最近一年使用:0次
2021-04-21更新
|
2622次组卷
|
11卷引用:黑龙江省嫩江市第一中学校等五校2020-2021学年高一下学期期末考试数学试题
黑龙江省嫩江市第一中学校等五校2020-2021学年高一下学期期末考试数学试题(已下线)【新东方】在线数学118高一下河北省石家庄市2020-2021学年高一下学期期末数学试题福建省莆田锦江中学2020-2021学年高一下学期期中考试数学试题(已下线)第20讲 期末复习(讲义)-【教育机构专用】2021年春季高一数学辅导讲义(沪教版2020必修第二册)(已下线)6.2.3向量的数乘运算(第二课时)-【高效导学】2021-2022学年高一数学下学期同步精品导学案(人教A版2019必修第二册)湖南省长沙麓山国际实验学校2022-2023学年高二上学期入学考试数学试题湖南省长沙市明德中学2022-2023学年高二上学期入学考试数学试题江苏省南京市第五高级中学2022-2023学年高一下学期4月期中数学试题四川省宜宾市宜宾市第四中学校2022-2023学年高一下学期期末数学试题广东省揭阳市普宁市华侨中学2022-2023学年高一下学期5月月考数学试题
名校
6 . 已知向量
,
,若
与
平行,则实数
的值为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b821a889623ac467c40df8af7bb7305f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01753295b0cce6911862b2c1ce674efc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b91254db5ff748150f449c5cdd256c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03d28588cd48a18ecfaa26f84464c578.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2021-03-30更新
|
1038次组卷
|
5卷引用:黑龙江省漠河市高级中学2020-2021学年高三上学期第三次摸底考试文科数学试题
黑龙江省漠河市高级中学2020-2021学年高三上学期第三次摸底考试文科数学试题重庆市第二十九中学2020-2021学年高一下学期期中数学试题(已下线)第8章 平面向量【真题训练】-2020-2021学年新教材高一数学下册单元复习一遍过(沪教版2020必修第二册)湖北省襄阳市第四中学2022-2023学年高二上学期新起点考试数学试题第六章 平面向量初步 尖子生必刷卷-2021-2022学年高一上学期数学 人教B版(2019)必修第二册
名校
解题方法
7 . 在
中,点
满足
,过点
的直线与
,
所在的直线分别交于点
,
,若
,
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e704292d4c8eef9ff9a634959d95e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3abd34df1150309cb07ac490e493abf8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd63c1b2b44374c2886a4651ccc53779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
![](https://img.xkw.com/dksih/QBM/2021/3/20/2682145962926080/2685620727635968/STEM/138838b8-5f34-4f76-8528-96664f6e3704.png?resizew=254)
您最近一年使用:0次
2021-03-25更新
|
428次组卷
|
3卷引用:黑龙江省密山市第一中学2020-2021学年高一下学期培优数学试题
名校
8 . 已知向量
,
,
,
,若
,则
的最小值______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/348156495aaee6b5b47d274733b34042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2925b9c4caf208af8f4450eed8c937de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e54834985ea41fcd7b9e41e2b1fe4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28c3d0b6c854a1a910f719c5a671db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43dd56f6c6a5155f34569ee6db8c7552.png)
您最近一年使用:0次
2021-01-09更新
|
5890次组卷
|
25卷引用:2016届黑龙江大庆实验中学高三考前训练一文科数学试卷
2016届黑龙江大庆实验中学高三考前训练一文科数学试卷2016届黑龙江大庆实验中学高三考前训练一理科数学试卷山东省日照市2017届高三校际联合模拟考试(三模)数学(文)试题山东省日照市2017届高三第三次模拟考试数学理试题山东省日照市2017届高三第三次模拟考试数学文试题山东省日照市2017届高三第三次模拟考试理科数学试题【市级联考】河南省八市2018-2019学年高二下学期第三次质量检测数学(文)试题湖北省黄冈市2019-2020学年高二上学期10月月考数学试题广西名校2019-2020学年高三上学期12月高考模拟数学(理)试题重庆市北碚区2019-2020学年高一上学期期末数学试题人教A版(2019) 必修第二册 过关斩将 第六章 平面向量及其应用 本章复习提升海南省北京师范大学万宁附属中学2019-2020学年度高一下学期开学考试数学试题山东省聊城市2020-2021学年高一下学期期中数学试题河北省任丘市第一中学2020-2021学年高一下学期第一次阶段考试数学试题山东省临沂市兰山区、兰陵县2020-2021学年高一下学期期中数学试题山西省潞城区第一中学校2020-2021学年高一下学期第一次月考数学试题2021年湖南省高中学业水平考试合格性考试仿真模拟数学试题(已下线)期末考测试(基础)-2021-2022学年高一数学一隅三反系列(人教A版2019必修第二册)云南省会泽县实验高级中学校2021-2022学年高一4月月考数学试题山东省济宁市泗水县2021-2022学年高一下学期期中考试数学试题广东省揭阳市惠来县第一中学2021-2022学年高一下学期第一次段考数学试题福建省厦门市湖滨中学2021-2022学年高一下学期期中考试数学试题陕西省商洛市镇安中学2022-2023学年高一下学期期中数学试题河南省新乡市封丘县第一中学2023-2024学年高一下学期开学测试数学试题河北省保定市唐县第一中学2023-2024学年高一下学期3月月考数学试题
名校
9 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
内一点
,过点
的两条直线
分别与椭圆
交于
和
两点,且满足
(其中
),若
变化时直线
的斜率总为
,则椭圆的离心率为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/098a3e7d1f1890863b7483a98b618119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ccf6bb5128017959d51ec3bc693c458.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1758ec2d7ee9c5a240900e00b3472ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
您最近一年使用:0次
2020-10-16更新
|
762次组卷
|
4卷引用:黑龙江省大庆实验中学2020-2021学年高二10月月考数学(理)试题
黑龙江省大庆实验中学2020-2021学年高二10月月考数学(理)试题(已下线)第44讲 解析几何中的极点极线问题-2022年新高考数学二轮专题突破精练江苏省南通市如东县2022-2023学年高二上学期10月阶段测试数学试题新疆维吾尔自治区喀什地区疏附县2023届高三上学期11月期中考试数学(理)试题
10 . 如图,在
中,
是
的中点,
,
是
上的两个三等分点
,
,则
的值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7177e98f4fd95cd1f73e8f8a9bf57ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c787ff3faf698f76331eda789b3ef912.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c37b6118f80d874d2c857fc9632977d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/f1ddc6c8-77b7-48e7-a5b6-0cc1f82f9573.jpg?resizew=182)
您最近一年使用:0次