1 . 四棱锥
的底面为矩形,
平面
,
在棱
上,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f6be38207f1b3af86e2f59bf08a195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a64c90c7546af879a6a96e9b4abc4d5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知空间向量
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a6a0c8f851443a3cf3f0845e1dc35ce.png)
A.![]() |
B.![]() ![]() ![]() |
C.若向量![]() ![]() ![]() |
D.向量![]() ![]() |
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2024-03-03更新
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2卷引用:福建省泉州市2023-2024学年高二上学期1月期末教学质量监测数学试题
2024高三·全国·专题练习
3 . 正四棱柱
中,底面
是边长为4的正方形,
与
交于点
与
交于点
,且
.
(1)用向量方法求
的长;
(2)对于
个向量
,如果存在不全为零的
个实数
,
,使得
,则称
个向量
叫做线性相关,否则称为线性无关.试判断
是否线性相关.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d912c3d63e7566f63a5d6820f9bb5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c7f786fc33d0506d64047034e12fd7a.png)
(1)用向量方法求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(2)对于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27bb33ccdad573e2b2b0e7facbcca07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75b5dc876d7dcd3c971b36d26668b1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a5eb204cdd638a40eded9c9d8453388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65237e0feff86664a9315cb175d30cac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a27bb33ccdad573e2b2b0e7facbcca07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7e84a3d14f243496cf60c7260cc1b42.png)
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2024·全国·模拟预测
4 . 已知正四棱柱
的底面边长为1,
,点P,Q分别满足
,
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cf96582bc4d56de6f4faa5dd1ca58ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ee5022b8de0e3b55c8d0cb1483b051.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1893b0ba3f5d6b242ad92164a57bf29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f2e48931276c19a08a9ed67823221e.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() |
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5 . 已知向量
,则
在
方向上的投影向量的坐标为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4986bbca24c0d876e716e9db868097df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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2024-01-05更新
|
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7卷引用:福建省泉州市实验中学2023-2024学年高二上学期1月考试数学试题
福建省泉州市实验中学2023-2024学年高二上学期1月考试数学试题四川省雅安市2023-2024学年高二上学期12月联考数学试题四川省部分名校2023-2024学年高二上学期期中联合质量检测数学试题广东省深圳市龙岗区华中师范大学龙岗附属中学2023-2024学年高二上学期期末区统考模拟考试数学试卷河北省石家庄市第二中学2023-2024学年高二上学期期末第一次模拟考数学试题宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末复习数学试题(一)(已下线)第3章 空间向量及其应用(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
6 . 若向量
,
,且
,则
在
方向上的投影向量是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2412c125e2f90b941a78f2958f2020f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a5b7fd1e042e60d12d05c87d4368ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c8c7eba950b5a1779860411feca302.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae98586d80f892771c90ab39eaced90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee437e6ff470c2f67b8429f57b90ae37.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 在空间直角坐标系中,向量
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f298e421179c4d9fba4a6f788a8cdbcd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ae984be4e927e1f24d6661d5a984ce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65de7c2f24ccd9a5a9b6c5920e981309.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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|
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8 . 在菱形纸片
中,E,F分别为
,
的中点,O是菱形
的中心,
,
,将菱形纸片
沿对角线
折成直二面角,以O为原点,
,
,
所在的直线分别为x轴、y轴、z轴,建立如图所示的空间直角坐标系,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](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/8d7bce5b3862e12e5c7d206c35052471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/828628c0876b45381c9a0edeb0fec236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/683c590673eece14fea3319c4fd5eb55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/4/c5524a79-7e5c-4f7d-af0b-ad2f1b3b74f6.png?resizew=160)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2卷引用:福建省泉州市安溪县2023-2024学年高二上学期11月期中考试数学试题
名校
解题方法
9 . 已知单位 空间向量
,
,
满足
,
.若空间向量
满足
,且对于任意实数
,
的最小值是2,则
在
,
所构成的平面内的投影向量的长度是_________ ;
的最小值是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccfda9afde4441cfd1d4df5fe9622d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6be4754cb0c8887d64a8c5a1660a962a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b78368814a178aa08fa204b0d8635d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98a655573947fe329096b21bc163097.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3697a03e7426158efa72de7b7419523c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17ccfda9afde4441cfd1d4df5fe9622d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0411792b587ddd3e04440392f011c224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95d660852c5226ff65a21cfb36b8b39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafafdc15aa4c9cf095d0258f04f4110.png)
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10 . 已知向量
,
,则向量
在向量
上的投影向量
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f810dbe61ee681f7d1e05e78c8771d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0a82691321ab5bd0c0d4d080779f15.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/e8af740e84814052ba6b234972eb5967.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-06更新
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544次组卷
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2卷引用:福建省南安市侨光中学2023-2024学年高二上学期第1次阶段考试数学试题