1 . 已知向量
,则向量
在
上投影向量的模为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbbbf2bc43f43feca55fa09e0c4e9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a06c8eae3652486cf9e416ce3a8ffc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
您最近一年使用:0次
名校
2 . 设
、
为两个随机事件,给出以下命题:
(1)若
、
为互斥事件,且
,
,则
;
(2)若
,
,
,则
、
为相互独立事件;
(3)若
,
,
,则
、
为相互独立事件;
(4)若
,
,
,则
、
为互斥事件;
其中正确命题的个数为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)若
![](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/a8e7b8749698633cd49782301cfc2f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d344fc34d910f3965df31da4d4b7d408.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677ac228b16598815a42812dbdf822ec.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7161327cdbe387412cb84d53ff9d681e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672d7bc529ccc16996c8c73a47f260d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aed1c8c2d3c89f9be006e0f73b7a54c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7161327cdbe387412cb84d53ff9d681e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672d7bc529ccc16996c8c73a47f260d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbd7a30952e451b004efdd97c216940e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ee035c6c34eef4268a150dab13117e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745870b7a13e889f50ad2ae9a8aa4649.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7161327cdbe387412cb84d53ff9d681e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/672d7bc529ccc16996c8c73a47f260d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d529ce919792f99e3792bb39f3c7dd1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
其中正确命题的个数为
您最近一年使用:0次
2024·全国·模拟预测
3 .
是直线
上的一个动点,
是圆
上的两点,若
均与圆
相切,则弦长
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbe0890043f34b4575bf7bb3a773e32b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
4 . 化简![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a13bd1975254eacb1c5c6b1f862214.png)
____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a13bd1975254eacb1c5c6b1f862214.png)
您最近一年使用:0次
解题方法
5 . 已知
是同一平面上的3个向量,满足
,
,
,则向量
与
的夹角为_____________ ,若向量
与
的夹角为
,则
的最大值为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa3610a990287d3ac756abae406540d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db24e47304fec964e8cb9278280046bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55fd756ebb1dd56415de2adbf33c0be0.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/b1760539b08d5c35caa5fe2c43a339f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20f69af6870bada879cddd7f6794d24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26abac73b9cb1af5c5d8e8c2dd136bbb.png)
您最近一年使用:0次
解题方法
6 . 已知
是定义域为
的偶函数,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6413b1c6404c92b9b900368e824336d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5215a578933ba72022450a6d3a37d14.png)
您最近一年使用:0次
名校
7 . 已知一个酒杯是由一个抛物线绕其对称轴旋转一周形成的,抛物线的方程为:
,现在将一个半径为
的小球放入酒杯中,若小球能触及杯子的最底部,则小球的半径
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ad5e6562cd44d9e80322ad8c35be93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2024-01-13更新
|
136次组卷
|
2卷引用:山东省菏泽市定陶区第一中学2023-2024学年高二上学期期末模拟数学试题
名校
解题方法
8 . 已知
且
,则
的最小值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22d812643e080d4d447fab7fe2ae2646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9182d60213e94c38b2ce9eabf6f02546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8586b9abdcfaa94d09a2631ee251cb.png)
您最近一年使用:0次
2024-01-13更新
|
676次组卷
|
3卷引用:福建省莆田市2023-2024学年高一上学期期末数学试题
名校
9 . 阿波罗尼斯是古希腊著名数学家,与阿基米德、欧几里得并称为亚历山大时期数学三巨匠,他研究发现:如果一个动点
到两个定点的距离之比为常数
(
,且
),那么点
的轨迹为圆,这就是著名的阿波罗尼斯圆.若点
到
,
的距离比为
,则点
到直线
:
的距离的最大值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2c77a42750684cb6157c2c7fb9422a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76218cf7a5779168198df12edafa276a.png)
您最近一年使用:0次
2024-06-11更新
|
47次组卷
|
2卷引用:青海省海东市第一中学2023-2024学年高二上学期期中考试数学试题
名校
10 . 在
中,
,
,
,
,
为
上一点,且满足
,若
,则
的值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1371fe98a65d8ebd840c8d98346b6d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5c9ba21933a3ac9f13936183443e8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b091c6a44e3ae2323c6830975471a137.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae64fb5b50398f3147e96e8648b3d5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72850427e83ff19a24305783e080b280.png)
您最近一年使用:0次