名校
解题方法
1 . 已知两个非零向量
与
的夹角为
,我们把数量
叫作向量
与
的叉乘
的模,记作
,即
.若向量
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4dda6a0ba7fbe7bacf15a5e63d8b9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4e6bae1b67a0a1eeafdd1114a792df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997d8a3acf19e132587e8115cd1384fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54eb5317665c796a0853517b7e9be9e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa27c09a5c955e423743bda656d0b50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8c759dbf3a4250335fbc1d24f9c9be3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af6a462c248f46fdbc9a7f8a5a4cf816.png)
A.![]() | B.10 | C.![]() | D.2 |
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3卷引用:山东省淄博市实验中学2023-2024学年高一下学期第一次模块考试(期中)数学试题
山东省淄博市实验中学2023-2024学年高一下学期第一次模块考试(期中)数学试题(已下线)专题03 平面向量的数量积常考题型归类-期末考点大串讲(人教B版2019必修第三册)河南省驻马店市新蔡县第一高级中学2023-2024学年高二下学期6月月考数学试题
名校
解题方法
2 . 已知点
,
,
,
.
(1)设线段AB的中点是H,若
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
________ ;
(2)已知
.若点Q的轨迹与直线
平行,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50edfb9ed0d50d6f35ad6a130208d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e717fc336c2b9c1617421b5b8a4ae6b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656de1832d5046c5c0d242372ff48c08.png)
(1)设线段AB的中点是H,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805e8f0e7b46332052b32f249b5df425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469ef1bfbac0fa50e8d54110b27ba46f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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3 . 已知函数
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39d4e199031b74357e9fbd723916fbc.png)
A.![]() |
B.![]() ![]() |
C.方程![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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名校
4 . 对任意两个非零向量
,
,定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2880d03a4fe19b30857292e07a7bb29d.png)
(1)若向量
,
,求
的值;
(2)若单位向量
,
满足
,求向量
与
的夹角的余弦值;
(3)若非零向量
,
满足
,向量
与
的夹角是锐角,且
是整数,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f7a1df960feef63dec4790d63f52279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b8a88a16125366536cb4ad658e0cf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2880d03a4fe19b30857292e07a7bb29d.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dba6c7eb6216014862640716991326a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22249dd883332a917ec68eaf7dd5ea23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb893d1367e26f4388ae4280f78630.png)
(2)若单位向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb0319e46d3d669c9439537e600c461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bca35e52b8430246a1cf96e9e617cce.png)
(3)若非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaaa5755983415a0dd11a44c4f426efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/189301a0467dfa2daf6b5806d15bfa22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dd1004f81418675f8cfac07219d59c.png)
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4卷引用:【高一模块三】类型1 新定义新情境类型专练
(已下线)【高一模块三】类型1 新定义新情境类型专练重庆市璧山来凤中学等九校联考2023-2024学年高一下学期5月月考数学试题吉林省部分名校2023-2024学年高一下学期联合考试数学试题(已下线)专题03 平面向量的数量积常考题型归类-期末考点大串讲(人教B版2019必修第三册)
解题方法
5 . 我国历史悠久,各地出土文物众多.甲图为湖北五龙宫遗址出土的道家篆书法印.图乙是此印章中抽象出的几何图形的示意图.如图乙所示,在边长为2的正八边形ABCDEFGH中,P是正八边形边上任意一点,则
的最大值是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab7aaa871ceb78e5b80b531a7cf4f1c9.png)
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6 . 已知□ABCD中,点P在对角线AC上(不包括端点A,C),点Q在对角线BD上(不包括端点B,D),若
,
,记
的最小值为m,
的最小值为n,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43bb3fb750948cd5eb2ee343d96c285c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a08557b7019b87fb3b4848527f59d5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/988bc9959a454f14decc997053ada91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/330914a84b8cc7d9fe5cba58ec1b7218.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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解题方法
7 . 如图,在矩形
中,过边
上的点
分别作
的垂线,分别交
于
,过
边上点
作
的垂线,分别交
于
,
,则集合
中的元素个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6029062c6a3c9b36225574d393489db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797e67927616b141ed7c6b83f8b6f4fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb45ab3ba0ec44779c85e32719f5d60d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee50575e3ebd56c4f46dd0bbf8e55d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4386d82eb8d40b0080aea374ecf6962c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9baa6286e8d3fee65fa15af683a227ac.png)
A.2 | B.4 | C.6 | D.8 |
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8 . ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994d6e7f47b3b98aa848c05d0af8f65e.png)
________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/994d6e7f47b3b98aa848c05d0af8f65e.png)
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名校
9 . 已知向量
的夹角
,且 ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d26a0c841ff72e442f1e661c18edf.png)
下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10814bc3db929e79874befe96cf4e3d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0211da37e92f915e781691296578ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/029d26a0c841ff72e442f1e661c18edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
A.若![]() ![]() ![]() |
B.![]() |
C.![]() |
D.![]() ![]() |
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名校
10 . 下列说法正确的是( )
A.在四边形![]() ![]() ![]() |
B.若![]() ![]() |
C.已知O为![]() ![]() ![]() |
D.已知![]() ![]() ![]() ![]() ![]() |
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