21-22高二·全国·课后作业
1 . 判断正误
(1)向量
与
的夹角等于向量
与
的夹角.( )
(2)若
,则
或
.( )
(3)对于非零向量
,
,
与
相等.( )
(4)若
,且
,则
.( )
(5)若
,
均为非零向量,则
是
与
共线的充要条件.( )
(1)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ed9c2e9fabbfc63733bae8fa079d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fdc83becc28e0f43d71427d9e8775d4.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7677fa4ecba4dd4005f5a1b52cf86b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49ffaae1b5eb029d0d726fdde99fe7c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a01b6bda6cc2edead3549796c95da81.png)
(3)对于非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce80d260d43c393191c6a6c8ba4f7472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ac54e22c9bfa5ffd711a583acfa634.png)
(4)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dfd95b2e1d2c7f2a85fffe24f62686d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a01b6bda6cc2edead3549796c95da81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec6df8a1e8ccc7a0dc182efa0a53cdb.png)
(5)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045899e47a20edeee3d7a9c60215765d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
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21-22高二·全国·课后作业
2 . 空间向量的数量积
(1)定义:已知两个非零向量
,
,则_________ 叫做
,
的数量积,记作
.即![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9afc7bfbc67ff08ae5380508d9ca746.png)
_________ .
【微提醒】零向量与任意向量的数量积为0.
(2)由数量积的定义,可以得到:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d6468ac363b1c2b09ecaf4d0533978.png)
_________ ;![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea3c0b6cf6f48d838dd08c07d06e693.png)
_________ .
(1)定义:已知两个非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0fe4d834e8eaca89ceaf9c64cdabd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9afc7bfbc67ff08ae5380508d9ca746.png)
【微提醒】零向量与任意向量的数量积为0.
(2)由数量积的定义,可以得到:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94d6468ac363b1c2b09ecaf4d0533978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bea3c0b6cf6f48d838dd08c07d06e693.png)
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21-22高二·全国·课后作业
3 . 投影向量
(1)在空间,向量
向向量
投影:
如图①,先将它们平移到同一平面
内,利用平面上向量的投影,得到与向量
共线的向量
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44debd1a82e235d29f93e395808b4854.png)
_________ ,称向量
为向量
在向量
上的投影向量.
(2)向量
在直线l上的投影如图②.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/20/5da5e1ea-9d33-4579-a56f-804b4a72c894.png?resizew=479)
(3)向量
向平面
投影:
如图③,分别由向量
的起点A和终点B作平面
的垂线,垂足分别为
,
,得到向量
,向量_________ 称为向量
在平面
上的投影向量.
(1)在空间,向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
如图①,先将它们平移到同一平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44debd1a82e235d29f93e395808b4854.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
(2)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/20/5da5e1ea-9d33-4579-a56f-804b4a72c894.png?resizew=479)
(3)向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
如图③,分别由向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/767ca1a587a1926cea9c9eeb55af4ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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2022-02-12更新
|
1011次组卷
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3卷引用:第一章 空间向量与立体几何 1.1 空间向量及其运算 1.1.2 空间向量的数量积运算
4 . 已知动直线l过点A(1,-1,2),和l垂直且与l的方向向量、
共面的一个向量为
,则P(3,5,0)到l的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edc29e6f02468674c8b1e9e54e15109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310bf80fa4269d4c7c85d205626f78d1.png)
A.5 | B.14 | C.![]() | D.![]() |
您最近一年使用:0次
2021-08-27更新
|
1783次组卷
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3卷引用:第十课时 课前 1.4.2.1 距离问题
第十课时 课前 1.4.2.1 距离问题(已下线)第07讲 向量法求距离、探索性及折叠问题 (高频考点—精练)人教A版(2019) 选修第一册 数学奇书 第一章 空间向量与立体几何 1.4.2 用空间向量研究距离、夹角问题 第1课时 用空间向量研究距离问题