名校
1 . 如图,已知
是边长为2的正三角形,P在边BC上,且
,Q为线段AP上一点.
,求实数
的值;
(2)求
的最小值;
(3)当
的重心在直线CQ上时,求
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6eef53cd73eb4a628ca6a95517131b12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bcd6acd78fc389ca2fe03c9006e4d32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa644477d812c38da6df9e3751468626.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2225e9d4e443d81abfe1bed83ba25e9b.png)
您最近一年使用:0次
2024-04-15更新
|
200次组卷
|
2卷引用:河南省河南名校联考2023-2024学年高一下学期4月月考数学试题
名校
2 . 如图,在
中,
,
,D,F分别为
的中点,P为
与
的交点,且
.若
,则
________;若
,则
________.则求解正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc03a3ba496faee748a8d63e5d4fa92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cca04b2a2b61d62a809776670a60c09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79b194152945f719c21bbe5d525338d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d426c98a712c3e5ddc8f2dff60efad2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edff1881635893293dd411ead8194aca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68e4de3cb03cd4c55fb031de5c063966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a11befb78a4346dba62561d3551584.png)
A.![]() ![]() | B.![]() ![]() | C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
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解题方法
3 . 已知
是同一平面内的三个向量,其中
.
(1)若
,且
,求
向量;
(2)若
,且
与
垂直,求
与
的夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a0a32446aed06817f5f72abf7fdae4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b18f32baa8e324b33d707f8d59e0a4f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e63aec503ed1d751bee61a5e0bab63c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd43c3c9a578b91fe832c4c2477103c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7d6c95e3dea8594de08776567a349cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437dc907211c5934f938d869f6b19e93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67a5673958e175b00200a75e645c73c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
您最近一年使用:0次
2024-04-14更新
|
456次组卷
|
2卷引用:河南省焦作市第一中学2023-2024学年高一下学期期中考试数学试题
解题方法
4 . 如图,
分别是等腰梯形
的边
上的动点,
,其中
为定值,
,设
,其中
.
,求出
的表达式;
(2)证明:
的余弦值与
的取值无关;
(3)求
的取值范围.
![](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/4ced9844fe2e052c70486af0740afa63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596d41b6556f383445536d1c534ac182.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1f07948e9258b482a2164ac871f90f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a18fec3e4a4fbc7b3e0e037ce650023.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d91513d2e546a5a0b5fd42379db8df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e72cf7374a65ced433b6fa113ef57d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e2be3e9225c71609248299caa49432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/192c2f1059f6e05d44df048f5fdca04b.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff7023ec0f513c7d0ef86859a5ede54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5db625151987f893816de66b15d9e699.png)
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解题方法
5 . 已知向量
,若
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa3ac8c05b8dd85f42aecf497380047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460e5ba67828c57daf2edb497fb52e56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.2 | D.4 |
您最近一年使用:0次
名校
6 . 已知向量
的夹角为
.
(1)求
;
(2)若存在实数
,使得
与
的夹角为锐角,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5bc463bbb149c0eca3dece73123b5d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(2)若存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12dfa2b2e9488107d07fdac71f433774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d108e523626be0b40be9b3543ce12524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2024-04-13更新
|
779次组卷
|
6卷引用:河南省周口市鹿邑县第二高级中学校2023-2024学年高一下学期月考测试(三)(6月)数学试题
河南省周口市鹿邑县第二高级中学校2023-2024学年高一下学期月考测试(三)(6月)数学试题黑龙江省绥化市绥棱县第一中学2023-2024学年高一下学期4月月考数学试题黑龙江省绥化市第二中学2023-2024学年高一下学期期中考试数学试卷黑龙江省九校联盟(齐齐哈尔五校+黑河四校 )2023-2024学年高一下学期4月期中联合考试数学试题(已下线)专题01 第六章 平面向量-期末考点大串讲(人教A版2019必修第二册)(已下线)专题03 向量的数量积-期末考点大串讲(人教B版2019必修第三册)
解题方法
7 . 如图,在
中,
为
边上一点,且
.
,求实数
的值;
(2)若
,求
的值;
(3)设点
满足
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4253aaba6bd1a82719bdc3fb0b8d1e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/810633059a470392035aa375dfc20fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e06ca53803f042a5eca99f56a70f05e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4822193151a92d1ab5cf2ced1e431ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a66e27ef92fcc51530e54533e23973.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6cfeef6dbc266f8ca53f78e7833e82d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca9b144a90e0a58c03398f066ec48861.png)
您最近一年使用:0次
名校
解题方法
8 . 在
中,已知
,
,
,BC、AC边上的两条中线AM、BN相交于点G.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/15/43417bdc-5b7d-40ab-a37c-80d441039b92.png?resizew=158)
(1)求
、
;
(2)求
与
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb8e20db1fbb40f17dea52f951b907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/15/43417bdc-5b7d-40ab-a37c-80d441039b92.png?resizew=158)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f580d157cf3e3b90c4c11a36e8fb467c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbd084e881d380464cc73aee4697f678.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/377962502ccf0435ed3bc89ec4fe594d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f8b2808877c3a2ec598fec709cfa579.png)
您最近一年使用:0次
2024-04-11更新
|
297次组卷
|
2卷引用:河南省焦作市第一中学2023-2024学年高一下学期期中考试数学试题
名校
9 . 如图,平面上A,B,C三点的坐标分别为
.
的坐标;
(2)如果四边形ABCD是平行四边形,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2af9f86ebe647e584ad01b75822cd96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d74a69d02c169c99d88f5fb3954526.png)
(2)如果四边形ABCD是平行四边形,求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2024-04-10更新
|
168次组卷
|
2卷引用:河南省周口市鹿邑县第二高级中学校2023-2024学年高一下学期月考(一)(3月)数学试题
名校
10 . 已知向量
.
(1)若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52337d6f53946db954d2d61e79c9099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,求实数
的值;
(2)若向量
满足
且
,求向量
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31a78b5a6055026f41ab65a96cc63dae.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c52337d6f53946db954d2d61e79c9099.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74716291e9b3c16bcd6b7e51b3a40e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337ab4dc61186ca58bb0605cb6d02df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bda62c4bf7ebc4226362e055d6e3af7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/842a5951171e63d5e31c7ab3e05423e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/337ab4dc61186ca58bb0605cb6d02df0.png)
您最近一年使用:0次
2024-04-10更新
|
482次组卷
|
4卷引用:河南省开封市五校(杞县高中等)2023-2024学年高一下学期4月期中联考数学试题