2024高三·全国·专题练习
1 . 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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解题方法
2 . 正方形ABCD中,
,点O为正方形内一个动点,且
,设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96643cc016e7e68f30c445bf47936a3.png)
(1)当
时,求
的值;
(2)若P为平面ABCD外一点,满足
,记
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91934cac6477909cf68ec266f562a397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96643cc016e7e68f30c445bf47936a3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7444214a631d3904f722bc05f07d0f0.png)
(2)若P为平面ABCD外一点,满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1909a3a6c9c51b7232cbf5acdfdc734.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c5b8a21ed3092f78d0c6c05267b635.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd288d4152caf5fc8187a1a901c8949f.png)
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2022-05-17更新
|
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5卷引用:福建省福州第一中学2021-2022学年高一下学期期末考试数学试题
21-22高二·湖南·课后作业
名校
3 . 下图是一个机器人手臂的示意图.该手臂分为三段,分别可用向量
,
,
代表.
代表整条手臂,求
;
(2)求
所代表的点与原点之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4dba1805a326f85d0eca6430bc14fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d56c6ef3478e21eeae9db1826f8bf110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52f6d5dc6cb53c7fbfd34f0855da33e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec655f610928ca21831e26645a21e99c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec655f610928ca21831e26645a21e99c.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec655f610928ca21831e26645a21e99c.png)
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6卷引用:福建省永安市第三中学高中校2023-2024学年高二上学期10月月考数学试题
4 . 已知空间有不重合的四点
.
(1)若
,求点
的坐标;
(2)若
是平面
的一个法向量,求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d28cc95f495a603774f765b656357f18.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/898393e05d74998ef205db39edbf4c99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ed9c2e9fabbfc63733bae8fa079d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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2021-08-31更新
|
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4卷引用:福建省德化第二中学2023-2024学年高二上学期第一阶段考试数学试题
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