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解题方法
1 . 在三棱锥
中,下列命题正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5d90f940f5693b22ddf2e7c761887d8.png)
A.若![]() ![]() |
B.若G为![]() ![]() |
C.若![]() ![]() ![]() |
D.若三棱锥![]() ![]() |
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7卷引用:江苏省常州高级中学2020-2021学年高二上学期期中数学试题
江苏省常州高级中学2020-2021学年高二上学期期中数学试题2021年北京大学基础学科招生考试数学试题北师大版(2019) 选修第一册 必杀技 第三章 2.2 课时2 空间向量的数量积(已下线)第02讲 空间向量基本定理(教师版)-【帮课堂】(已下线)习题 3-2福建省莆田市第五中学2023-2024学年高二上学期月考(一)数学试卷 (已下线)专题02 空间向量基本定理及其坐标表示压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)
18-19高三上·上海·期中
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2 . 定义向量的外积:
叫做向量
与
的外积,它是一个向量,满足下列两个条件:
(1)
,
,且
,
和
构成右手系(即三个向量两两垂直,且三个向量的方向依次与拇指、食指、中指的指向一致);
(2)
的模
(
表示向量
、
的夹角);
如图,在正方体
,有以下四个结论:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/58c53ce7-eff6-4b61-ab7f-504b979c0a88.png?resizew=143)
①
与
方向相反;
②
;
③
与正方体表面积的数值相等;
④
与正方体体积的数值相等.
这四个结论中,正确的结论有个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f9924630c2d61af394ff7464e842fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb2eb0f56b8b2259015bfc21efae0ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bedeb46904acda91f92295dc8ff1323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f9924630c2d61af394ff7464e842fd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03f9924630c2d61af394ff7464e842fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42a654bf8a50c7041b123109d28bd54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7166dfb77adcc150f8cf7688e53fa876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
如图,在正方体
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/58c53ce7-eff6-4b61-ab7f-504b979c0a88.png?resizew=143)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1b1f9ed57243ed8b99f72301eaaad15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6361249877a88f60d4b3bb71ef7b5517.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200833e4ac25379efc09da3e2641c2f4.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296fe8642d20cfbc7aaec15e01a03b4c.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f750f7bf53bca76deb86d9399e08e010.png)
这四个结论中,正确的结论有个
A.4 | B.3 | C.2 | D.1 |
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3 . 如图所示,二面角
为
,
是棱
上的两点,
分别在半平面内
,且
,
,
,
,
,则
的长______ .
![](https://img.xkw.com/dksih/QBM/2019/3/26/2169054127112192/2170394739605504/STEM/5df431a791a94542945db47ba30ddd12.png?resizew=246)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/754bbd99327195520a4ca3ce3b9a0577.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b3c032441543354c154ee67d744abb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c638fb895acd987140d0ca6bef097499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb0a2d7d40a6c0bf1fddb802db381689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71e6ea7333dbc78d0a7b9bc3892f940.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/2019/3/26/2169054127112192/2170394739605504/STEM/5df431a791a94542945db47ba30ddd12.png?resizew=246)
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7卷引用:【校级联考】湖北省宜昌市(宜都二中、东湖高中)2019届高三12月联考数学(理)试题
4 . 已知
均为非负实数,且
,则
的取值范围为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9defa23d2a9b88f4dd10e0ea4bef2189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/957a01feab0c269c29ed0bbc05d5d5e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b7078b2394a48ac2a9ec3484e27cf1c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:【全国市级联考】浙江省宁波市2018届高三5月模拟考试数学试题
【全国市级联考】浙江省宁波市2018届高三5月模拟考试数学试题(已下线)06练-冲刺2020年高考数学小题狂刷卷(浙江专用)浙江省杭州地区四校2018-2019学年高三上学期联考数学试题2020年浙江省名校高考仿真训练卷(四)
5 . 【2018届浙江省宁波市5月模拟】已知一个三棱锥的三视图如图所示,其中俯视图是顶角为
的等腰三角形,侧视图为直角三角形,则该三棱锥的表面积为____ ,该三棱锥的外接球体积为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29c31a46b9780b063b83f65d68e4671b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/14494d93-0edf-4126-afe5-b50ed5fe39b7.png?resizew=196)
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6 . 如图,一块均匀的正三角形的钢板的质量为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e233fe2b29b0bb1e01409dfe0829fe.png)
,在它的顶点处分别受力
,
,
,每个力与同它相邻的三角形的两边之间的角都是
,且
.要提起这块钢板,
均要大于![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e233fe2b29b0bb1e01409dfe0829fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a541551402a5fadca4831fe902e95c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1282962a17a48a18edf733204054d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1f8b853edf78fc3eb0d14010514892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7357a34a8802d52df9d38d3b6b58388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a541551402a5fadca4831fe902e95c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/2016/12/2/1573193837322240/1573193843228672/STEM/50a7321b-bc75-43ee-8ccf-970a5ee26aca.png?resizew=171)
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7 . 已知
=(2,1,﹣3),
=(﹣1,2,3),
(7,6,λ),若
,
,
三向量共面,则λ=
![](https://img.xkw.com/dksih/QBM/2015/1/27/1571971155877888/1571971161522176/STEM/270eabc694644cef84cd331ed17b84b7.png)
![](https://img.xkw.com/dksih/QBM/2015/1/27/1571971155877888/1571971161522176/STEM/289dfd57b62b45919a3b2f4d64a8cd41.png)
![](https://img.xkw.com/dksih/QBM/2015/1/27/1571971155877888/1571971161522176/STEM/851d6adee0c54472bd47d788db91cb7b.png)
![](https://img.xkw.com/dksih/QBM/2015/1/27/1571971155877888/1571971161522176/STEM/270eabc694644cef84cd331ed17b84b7.png)
![](https://img.xkw.com/dksih/QBM/2015/1/27/1571971155877888/1571971161522176/STEM/a3f90a8e2ff64179b401d694e33714d5.png)
![](https://img.xkw.com/dksih/QBM/2015/1/27/1571971155877888/1571971161522176/STEM/32bceefae1ca47a38f2fd11501e101ec.png)
A.9 | B.﹣9 | C.﹣3 | D.3 |
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3卷引用:专题8.6 空间向量及其运算和空间位置关系(精练)-2021年高考数学(理)一轮复习学与练
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