1 . 如图所示,在平行六面体
中,
为
与
的交点,若一组基底为
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d1b000652db5cf562b3e0711f6a6b7a.png)
_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d1b000652db5cf562b3e0711f6a6b7a.png)
![](https://img.xkw.com/dksih/QBM/2023/12/21/3394101824905216/3394907847999488/STEM/44fcb7c7f2a2446289d4d3ba4cac17b6.png?resizew=194)
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2 . 已知
,若
,则
的坐标是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5437f850543536910cc2a1c271312e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12775390b9fb8f742175c95ead65df0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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3 . 在三棱锥
中,
在线段
上,满足
是平面
内任意一点,
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656a93925561a68ac02e7352c933085c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f98d6d60d31af127291c3d22a7aa5b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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2023-11-25更新
|
538次组卷
|
5卷引用:四川省成都市树德中学2023-2024学年高二上学期期中考试数学试题
四川省成都市树德中学2023-2024学年高二上学期期中考试数学试题四川省内江市第二中学2023-2024学年高二上学期12月月考数学试题(已下线)专题01 空间向量与立体几何(1)(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)山东省枣庄市滕州市2023-2024学年高二上学期期末数学试题
4 . 如图,在平行六面体
中,
, ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0c46783b77cce2bd4b45b9acc61884.png)
则
=____ ,
=____ (
,
精确到0.1).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ecd2fb9d59e0d9a46ea3062f566ff40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0c46783b77cce2bd4b45b9acc61884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369056cce7ae550158fa9c1c7772da59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8bad16b7cdf8c638cd324f5be5d834f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fc42fb48159c7259b66a719faa60459.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/721554f715d299b5e1974e58aae90897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df276e9b9424486d59c747f1227b213c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/8/c723fe5c-1995-442e-a813-ac30bfc335c9.png?resizew=156)
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5 . 已知
、
、
为空间中三个单位向量,且
、
、
与
夹角为
,点P为空间一点,满足
且
,则
最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4876efa91f38d11ce12fed2e1fbf2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d514783895850481ebcb10d8b8354884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef8337706c550bc095d7a2bd872221a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/231b861d6d1f1d0b9f52b041cb40eb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6dfcefb063de42c54340b4378dfee89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b08927eb957325eead728098d7c61587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49eaf009bccbdd52b1a9817a8a3e5e23.png)
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6 . 定义:设
是空间的一个基底,若向量
,则称有序实数组
为向量
在基底
下的坐标.已知
是空间的单位正交基底,
是空间的另一个基底,若向量
在基底
下的坐标是
.则向量
在基底
下的坐标是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e566988b6fab97d461876e88efd0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd33a4fb7ee6987a540f96ff057b7b84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b525d8c768efd801ab58bc4c0da9221e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4478fcaef66e8a6a96925ce12d0f8e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83e566988b6fab97d461876e88efd0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5401d7f4a297c8b097e74bdebaaa8570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82eedc2d1529ca318b38f6a9a3065a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4478fcaef66e8a6a96925ce12d0f8e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82eedc2d1529ca318b38f6a9a3065a03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9d567af011a49b2ab880c904dd2637b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4478fcaef66e8a6a96925ce12d0f8e8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5401d7f4a297c8b097e74bdebaaa8570.png)
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7 . 如图,两个正方形ABCD,CDEF的边长都是6,且二面角
为
,M为对角线AC靠近点A的三等分点,N为对角线DF的中点,则线段MN=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d76403bac26df50d934d93586f8a11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
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2023-09-17更新
|
1036次组卷
|
9卷引用:江苏省郑梁梅高级中学2022-2023学年高二下学期期中数学试题
江苏省郑梁梅高级中学2022-2023学年高二下学期期中数学试题湖南省永州市宁远县第二中学2023-2024学年高二上学期9月联考数学试题河北省衡水市第十四中学2023-2024学年高二上学期一调数学试题内蒙古乌兰察布市四子王旗宽高实验学校2023-2024学年高二上学期期中数学试题四川省绵阳南山中学2023-2024学年高二上学期期中考试数试题安徽省合肥市第一中学2023-2024学年高二上学期素质拓展训练(10)数学试题山东省临沂市平邑县平邑县第一中学2022-2023学年高二上学期10月月考数学试题(已下线)专题 01 空间基底及综合应用(3)(已下线)专题 01 空间基底及综合应用(4)
名校
解题方法
8 . 如图,已知平行六面体
中,
,
,
.
为
的中点,则
长度为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd694ad3a4733c7c84aaa7946aeea4de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a66200ae44919a57caf401a6d47737ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2555ddf0e1c249150fd1873e75d1420.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20f758b78070af2142f7d26d56a769b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094e639c2b31dc54b1b3e6456e77843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1165830b314a0dab65ea267e82bd3f6.png)
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2023-07-28更新
|
691次组卷
|
4卷引用:江苏省扬州市宝应县2022-2023学年高二下学期期中数学试题
9 . 在三棱柱
中,点
在线段
上,且
,若以
为基底表示
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6285803e186abb615e9add52034bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b104831ce8f0486de0faf40d5b24d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
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2023-06-29更新
|
447次组卷
|
3卷引用:江苏省淮安市2022-2023学年高二下学期期末数学试题
名校
解题方法
10 . 如下图,在三棱锥
中,设
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8926ddd0b69d714c7310cc5bf23d199d.png)
________________ .(用
表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352afb2166bc2d282d55bd7bba4388e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bb9c0835434fb96cbda8370c92d85c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8926ddd0b69d714c7310cc5bf23d199d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e12e95f703ad30ab9a3d38376830989.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/7/63936335-3a64-4e78-abe4-26dbb03274e4.png?resizew=151)
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