名校
解题方法
1 . 在矩形
中,
,
,
是
的中点,
是
边上的三等分点(靠近点
),
与
交于点
.
(1)设
,
,请用
,
表示
和
;
(2)求
与
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa2b5e09f8ec785c59900a529390a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.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/d5c3accb1b8a5479439beff4259660e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8c53645db602c72b00b599c2c0ff97.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c16ed731b0f6ff2d7423c5e3f83cccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbaeb91bfb21e7bb048e527d355b637c.png)
您最近一年使用:0次
2023-07-09更新
|
261次组卷
|
2卷引用:福建省泉州市2022-2023学年高一下学期期末教学质量监测数学试题
2 . 已知向量
,
.
(1)若
∥
,求
;
(2)若
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f4dcf415977dea53f52a85b6b82136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd653f0414e1c9dcfb3ec06aa2881da5.png)
(1)若
![](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/a6e1ac68aa01c4bfbeef78b366075ae3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19e9066e6ebe86de2108970c51a8b88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c44e791585f0c5a465df424e349d1d7d.png)
您最近一年使用:0次
2023-06-28更新
|
433次组卷
|
3卷引用:江苏省徐州市2022-2023学年高一下学期期末数学试题
名校
解题方法
3 . 如图,已知斜三棱柱
中,平面
平面
,
与平面
所成角的正切值为
,所有侧棱与底面边长均为2,D是边AC中点.
(1)求证:
∥平面
;
(2)求异面直线
与
所成的角;
(3)F是边
一点,且
,若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61cdaadeae37736a1e6dd93fa1fe712f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3aace91caec728e174daec29a3568ae.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/30/1c05cdba-2179-49f6-b923-bc0f589b7092.png?resizew=204)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bf9628142422a4884bd59538da6d312.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
(3)F是边
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4633c8d720b79fbd51094e000fd53a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58e57df2381ec2af9a8516a9fa28b695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2023-06-28更新
|
926次组卷
|
2卷引用:江苏省南京市六校联合体2022-2023学年高一下学期期末联考数学试题
名校
解题方法
4 . 已知
,
,
.
(1)若
,求
的值;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db12e32ec95af7a916cd136fd21afc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99043a7ca7766a45fca34ce0fb59edaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae470980d6e3b53c65b9d42d1f011c5.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7796cec50ed668e457ae5398295533af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e496ee7d3685671a6c9dcf1821c58c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/483053da66e1cdcd910c4b24f72bfd2b.png)
您最近一年使用:0次
2023-06-27更新
|
302次组卷
|
3卷引用:江苏省南京市江宁区2022-2023学年高一下学期期末数学试题
名校
5 . 如图,在△OAB中,P为线段AB上的一个动点(不含端点),且满足
.
![](https://img.xkw.com/dksih/QBM/2023/6/20/3263775063826432/3267196066807808/STEM/4452bdc0cd5e4b49aaabbd4ab9957496.png?resizew=158)
(1)若
,用向量
,
表示
;
(2)在(1)的条件下,若
,
,且
,求
的值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://img.xkw.com/dksih/QBM/2023/6/20/3263775063826432/3267196066807808/STEM/4452bdc0cd5e4b49aaabbd4ab9957496.png?resizew=158)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.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/91174b2336306191ba275a87864172b7.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45252e14150ec0959437856eb30ef624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a600402d668cfc808ecb2cbd990f9f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ff5c21185c13eae675906dabd3593c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a66e27ef92fcc51530e54533e23973.png)
您最近一年使用:0次
2023-06-25更新
|
1141次组卷
|
4卷引用:四川省成都市成都外国语学校2022-2023学年高一下学期期末数学试题
名校
解题方法
6 . 在
中,
,
,M点为BC的中点,N点在线段AC上且
,
.
(1)求AC;
(2)若点P为AM与BN的交点,求
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba03505a2ec6653c4a65830d61694c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a07a68f3e85fe37916fb89f2f09ffa36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd1b3c262e8bf58c8479708d7496bbcd.png)
(1)求AC;
(2)若点P为AM与BN的交点,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45a8a837c11c07073da3ff751d70278.png)
您最近一年使用:0次
2023-06-21更新
|
587次组卷
|
2卷引用:广东省佛山市禅城区2023届高三模拟预测(二)数学试题
名校
解题方法
7 . 已知向量
,
.
(1)若
,求实数k的值;
(2)若
与
的夹角是钝角,求实数k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/779d3b960e7c55f1eb8182e21f16bd4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f49f461d57d35cebe267f62f2c5ec1f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5307169f49ce3173e84eb5275cd3cbc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
您最近一年使用:0次
2023-06-21更新
|
614次组卷
|
5卷引用:江苏省淮安市楚州中学、新马高级中学2022-2023学年高一下学期5月第二次联考数学试题
江苏省淮安市楚州中学、新马高级中学2022-2023学年高一下学期5月第二次联考数学试题湖南省湘潭钢铁集团有限公司第一子弟中学2022-2023学年高一下学期期末数学试题(已下线)考点巩固卷12 平面向量(十二大考点)陕西省渭南市蒲城中学2023-2024学年高二上学期9月开学考试数学试题(已下线)专题3 平面向量的应用(期中研习室)
8 . 如图,
的坐标分别为
,
,
,
,
分别为
的重心、外心.
(1)写出重心
的坐标;
(2)求外心
的坐标;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c05e8c15c3c50b19c36c90bb1be9e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae29b64cbfccdc15fff07e26294a7b5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7204f43679af6935e494c59d40c6ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/12/1a491542-37b5-46ce-ae76-04fc9618910c.png?resizew=182)
(1)写出重心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(2)求外心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
您最近一年使用:0次
名校
9 . 如图,在
中,
,点E为
中点,点F为
上的三等分点,且靠近点C,设
.
表示
;
(2)如果
,且
,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0019a40382ab3b0ed0b127f75eabe48b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3ceac772dba008adf20e589703bd7e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137b014134c70cbd1338a583c4355243.png)
(2)如果
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae59172207d0d8c85073fa2bd093705c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316c97c5b6f7c0fbdf7b9e4b9fccb661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdddaf04139a84bb1f64fc9baa414497.png)
您最近一年使用:0次
2024-03-28更新
|
941次组卷
|
17卷引用:广东省深圳市2020-2021学年高一下学期期末数学试题
广东省深圳市2020-2021学年高一下学期期末数学试题广东省肇庆市第一中学2021-2022学年高二上学期开学考试数学试题福建省永定第一中学2022-2023学年高一下学期第一次阶段考试数学试题广东省深圳外国语学校高中园2022-2023学年高一下学期期中数学试题广东省佛山市南海区九江中学2022-2023学年高一下学期第三次大测数学试题(已下线)模块三 专题5 大题分类练(平面向量)基础夯实练(北师大版)(已下线)模块三 专题4 大题分类练(平面向量)基础夯实练(人教A)广东省惠州市惠阳区第五中学、惠阳叶挺中学2022-2023学年高一下学期3月月考数学试题(已下线)模块三 专题4 大题分类练(平面向量)基础夯实练(苏教版)江苏省南通市通州区金沙中学2022-2023学年高一下学期3月质量监测数学试题江苏省苏州吴江高级中学2023-2024学年高一下学期3月月考数学试题上海市建平中学2023-2024学年高一下学期期中教学质量检测数学试题江苏省无锡市辅仁高级中学2023-2024学年高一下学期期中考试数学试题福建省厦门外国语学校2023-2024学年高一下学期期中考试数学试卷上海市朱家角中学2023-2024学年高一下学期第二阶段质量检测数学试题(已下线)专题05向量数量积期末10种常考题型归类-《期末真题分类汇编》(人教B版2019必修第三册)江苏省无锡市辅仁高级中学2023-2024学年高二下学期期中考试数学试题
名校
解题方法
10 . 已知
的内角
的对边分别为
,向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1796bb18cc55270eed9432040a4d774f.png)
,且
.
(1)求角![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b995fcd47faee2e939ef2e47813cd6.png)
(2)若
的面积为
,求
的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7af7c5df749c6fa9bbe87faa72c66d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f2599ca8b6b683e57a82699c8b1ebb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1796bb18cc55270eed9432040a4d774f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42fdfc65abe0768bdc6c94162500f19a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014a82692e31ac1980b50100c919254c.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7b995fcd47faee2e939ef2e47813cd6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b93a6d262d95ff5e93ac0a349aed6822.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
2023-06-03更新
|
863次组卷
|
9卷引用:安徽省定远中学2023届高三下学期考前押题数学试卷
安徽省定远中学2023届高三下学期考前押题数学试卷云南省曲靖市民族中学2022-2023学年高二下学期5月月考数学试题陕西省宝鸡教育联盟2022-2023学年高二下学期期末文科数学试题山西省金科大联考2023-2024学年高二上学期9月月考数学试题湖北省恩施州巴东县第一高级中学2023-2024学年高二上学期第一次月考数学试题湖北省A9高中联盟2023-2024学年高二上学期期中联考数学试题河南省河南名校联考2023-2024学年高一下学期4月月考数学试题贵州省六盘水市盘州市第一中学2023-2024学年高二上学期期中模拟考试数学试题云南省曲靖市马龙区第一中学2023-2024学年高一下学期3月月考数学试题