已知
,
,
是同一平面的向量,其中
是单位向量,非零向量
与
的夹角为
,向量
满足
,则
的最小值是__________ .
![](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/3dc64abe49847ade9b78678ba1f8e0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc64abe49847ade9b78678ba1f8e0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc64abe49847ade9b78678ba1f8e0e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c936cc3a7aa0bcdfea15977d4ffe51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5382bd3fda4371289ce6800f71f9565.png)
更新时间:2024-05-24 00:35:36
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相似题推荐
填空题-单空题
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较难
(0.4)
名校
【推荐1】向量集合
,对于任意
,以及任意
,都有
,则称S为“C类集”,现有四个命题:
①若S为“C类集”,则集合
也是“C类集";
②若S,T都是“C类集”,则集合
也是“C类集”;
③若
,
都是“C类集”,则
也是“C类集”;
④若
,
都是“C类集”,且交集非空,
,也是“C类集”.
其中正确的命题有____________________ (填所有正确命题的序号).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41bbea48a9e8cdc6e591bdc85ef6cdda.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2cd5b73e6422370539a64e009edb741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e756357aaab202398e6cded445f9caeb.png)
①若S为“C类集”,则集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df8ade2d8330ac61c4192cfd1df19fc0.png)
②若S,T都是“C类集”,则集合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194bad922d5bc98b6a7e51ae35f67d54.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2646f41226f24960a6186dc7860ef45.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b76d26b78e63683dfacf10d3da6d74d.png)
其中正确的命题有
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【推荐2】如图,已知
中,点
在线段
上,点
在线段
上,且满足
,若
,
,
,则
的值为__________ .
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/7a661750abcc45e9953581e11d683378.png?resizew=45)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/cb7958677c014daab460ccf64ad9b359.png?resizew=21)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/1f7d0a786b18405487bcbe86c323b4fa.png?resizew=28)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/86e7079bf8674b61810cbfce1dce22cc.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/47c4948cc8944bf3a09eed7e058734f4.png?resizew=31)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/a14bc71b92f347f286786bbd31d78dc9.png?resizew=101)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/8a23d6cca6024b2c98cd5d7979415960.png?resizew=56)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/c4e9a797c56a4f24abed704f7f006c30.png?resizew=55)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/672eaafc93744f1ea3ff50b49ac001a3.png?resizew=93)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/955e280aa8e6449f9e1acf26424dc8d1.png?resizew=60)
![](https://img.xkw.com/dksih/QBM/2018/1/6/1854394921328640/1855458432696320/STEM/b5c168f2d9594d9cbd742ce5a4997e06.png?resizew=253)
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解题方法
【推荐1】已知
的面积为3,
,
为
所在平面内异于点
的两个不同的点,若
且
,其中
,则
的面积为______ .
![](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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d5bc7da11e313e3b887d34d41b99473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbb5a7b16c8dcaf514a7555d5a0ee866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
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【推荐2】平面向量
满足:
,且
.则
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed41eea5886ac2958e0f8cd14cdbb54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6fb061cfce0487a0c0e5b1f8e66ebd6.png)
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