名校
1 . 已知平面向量
,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324c671a35160441f7669e02e876dae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a6a613f8b0e32fb71902f50f30ca4d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
A.![]() | B.![]() | C.![]() | D.1 |
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2 . 下列命题正确的是( )
A.已知![]() ![]() ![]() ![]() ![]() ![]() |
B.在![]() ![]() ![]() ![]() |
C.已知![]() ![]() |
D.已知![]() ![]() ![]() ![]() ![]() |
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解题方法
3 . 已知平面向量
.
(1)若
,求
;
(2)若
,求向量
与
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7287bb13fc21423c00c2a0b4435546d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b904789c43cb34d62bc40a4d8773735d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72cfe95f520c7b454ceabb2ae9af0a87.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13649cba7128ac8ec908fe28e38b4545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
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2024-04-18更新
|
933次组卷
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5卷引用:安徽省亳州市第一中学2023-2024学年高一下学期期中检测数学A卷
安徽省亳州市第一中学2023-2024学年高一下学期期中检测数学A卷安徽省亳州市第一中学2023-2024学年高一下学期期中检测数学B卷四川省达州市万源中学2023-2024学年高一下学期4月期中考试数学试题(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)四川成都实验外国语2023-2024学年高一下学期期中考试数学试题
名校
4 . 如图所示,在边长为3的等边三角形ABC中,
,且点P在以AD的中点O为圆心,OA为半径的半圆上,若
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a81889370d45239939a36de53c4445d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95d146bdcc8ac0a256c12696e9b9826.png)
A.![]() | B.![]() ![]() |
C.![]() | D.![]() |
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5 . 下列说法中正确的是( )
A.向是![]() |
B.![]() |
C.两个非零向量![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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6 . 下列四个命题正确的是( )
A.若![]() ![]() |
B.若复数![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.在![]() ![]() ![]() ![]() |
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解题方法
7 . 如图,在梯形
中,
,
,
,点
分别为线段
,
上的三等分点,点
是线段
上的一点.
的值;
(2)求
的值;
(3)直线
分别交线段
于M,N两点,若B,N,D三点在同一直线上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/762f99edee52c4984ba077facc51d8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f864244952b60f3648f08a19268efae9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cffa64009879efc50d310d24052fe5c8.png)
(3)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4572fa04373cd8e1e005a2f34f3953.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c1292487839550e3724ba9c2eee94e.png)
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2024-04-10更新
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8 . 如图,在
中,已知
,M是
的中点,N是
上的点,且
相交于点P.设
.
,试用向量
表示
;
(2)若
,求实数x的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d87aaec0ff6ebe697a942feaed39ddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04a66f3b2ee90819abbd18dcf0543a8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ba495e8f9fe02229a4248fdbfb4710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fac9575a5985527e283f7295fdaf72c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6c25c8513bd15674f632b46d5a926.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e4ece75fe9b8555909be5a00d2b7af0.png)
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9 . 如图所示,点P,Q分别位于边长为1的正方形
的边
上,
,记点
为
的外心,若
,则
的最大值为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfbeb7390ee66d7b126812483a3152e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e13889db9188c455a3ac91f2f32cf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48e91eeb57e4fc87e26efb7d371f6f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/8/3e27b6a2-e055-4518-ab68-58ca764a7e9b.png?resizew=150)
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解题方法
10 . 在
中,已知
,
,
,AC边上的中线为BN,M为BC边上靠近B的四等分点,连接AM交BN于点P.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/b352d10c-6ceb-4f56-8755-93dc43ec5af1.png?resizew=190)
(1)用
与
表示
,并计算AM的长;
(2)求∠NPM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/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/b352d10c-6ceb-4f56-8755-93dc43ec5af1.png?resizew=190)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
(2)求∠NPM的余弦值.
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