名校
解题方法
1 . 已知
,则
的最小值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4d01d5cb535c537b2d0a8c854651516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a61cd9a7a66e97c4b889ffad4eb825.png)
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2024-05-28更新
|
540次组卷
|
2卷引用:山东省济宁市2024届高三下学期三模数学试题
名校
2 . 在
中,
,
,
的外接圆为圆O,P为圆O上的点,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7578b53de65f7d7770ddc7e80a5e395e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07f536964d96829a5d2d8e48c386877d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59880e470359d8e9faf6ae5ce155cf2a.png)
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2024-04-22更新
|
853次组卷
|
3卷引用:山东省济宁市第一中学2023-2024学年高一下学期5月期中测试数学试题
名校
解题方法
3 . 如图,半径为1的扇形
中,
是弧
上的一点,且满足
分别是线段
上的动点,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a77343ecde1c2665df291761b6563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35945d2fac67566267a26b514a2f1183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd7a5191e13cb6475878df8b71413ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d8eb37a4dd75318dcbd836395e575bd.png)
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2024-04-19更新
|
620次组卷
|
2卷引用:山东省实验中学2023-2024学年高一下学期第一次阶段测试(3月)数学试题
名校
解题方法
4 . 如图,圆
是
的外接圆,
,
,
,若
,则
的最大值是__________ .
![](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/17d43145fd23afecf7741c417362da76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/737776cad8215cdcb2a7e2f68fd1673c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb370f9f62b28ff9ea09da2d3934c9c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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名校
解题方法
5 . 在
中,已知
为边
上一动点,过点
作一条直线交边
于点
.
为
中点,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d013a2e6f2f1c81e57d3902d8b619a6.png)
______ .
(2)设
,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed53658fbade8d8a42e76fc982eced8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8feb746c04bd5c9311260ea61bb1011.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894706f45d576906aca6acaea15634ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d013a2e6f2f1c81e57d3902d8b619a6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e050512dccc00f7906dd25aae90635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd5cf9e918c0a1c676378b2d7e801c8f.png)
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名校
解题方法
6 . 我国人脸识别技术处于世界领先地位.所谓人脸识别,就是利用计算机检测样本之间的相似度,余弦距离是检测相似度的常用方法.假设二维空间中有两个点
,
,O为坐标原点,余弦相似度为向量
,
夹角的余弦值,记作
,余弦距离为
.已知
,
,
,若P,Q的余弦距离为
,Q,R的余弦距离为
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a2b8dae45cd30a752aedb1ca66c30a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.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/1df320d266e857a428ff0bac1eb680bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2376fa0549e6fae46bae54d6ace942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926778fe15991308849cdba1822595a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1b00c13a8bb6db096dd866a2c37dee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20bb38fbd8ff8e5f8e985a0babf498d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e28a96ee1e62b7fbc1fb0257ad0deeed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06a2b8dae45cd30a752aedb1ca66c30a.png)
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2024-04-04更新
|
530次组卷
|
3卷引用:山东省临沂市第二中学2023-2024学年高一下学期第一次阶段性测试数学试题
解题方法
7 . 已知
五个点,满足:
,
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8bbd4a50586fb5286f33b5a92301752.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b4d624494ccde052011eb6a7937c717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094ea26d26c99ca5eca5c8800d964657.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dee9261554a7f9d07fc9162c95afa16.png)
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2024-03-22更新
|
709次组卷
|
6卷引用:山东省菏泽市第三中学2024届高三下学期3月月考数学试题
山东省菏泽市第三中学2024届高三下学期3月月考数学试题新疆乌鲁木齐地区2024届高三第二次质量监测数学试题(已下线)高一 模块3 专题1 第4套 小题进阶提升练(已下线)高一 模块3 专题1 第4套 小题进阶提升练(苏教版)(已下线)压轴题06向量、复数压轴题16题型汇总-1福建省南安市蓝园高级中学2023-2024学年高一下学期期中考试数学试题
名校
解题方法
8 . 已知是锐角三角形
的外接圆圆心,
,若
,则
的值为
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名校
解题方法
9 . 已知向量
,满足
,若对任意模为
的向量
,均有
,则向量
的夹角的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb371bd7728c6d6a16533a93924ad998.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ccb6028d04a5d64022e801619a09622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b8da3bf4a7f784df75158457e60a52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
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23-24高三上·山东德州·期中
解题方法
10 . 已知平面向量
,
,
满足:
,
,
,
,则向量
,
的夹角为______ ;向量
在向量
上投影数量的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07fed6074d3273a20a13eafd01a7e51a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ff265969988f1f138700129e5d7a6d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e306fc148916f732db183d4db5e84b3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5ccbbd8796a4a41e938368ecb59487.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
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