名校
1 . 如图,平行六面体
各条棱长均为1,
,
,则线段
的长度为_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a674aa2ce5caabcad5abe65b5402ce6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/990e1874-d36e-442f-a1b6-fd390f5bf6b8.png?resizew=188)
您最近一年使用:0次
2023-12-22更新
|
403次组卷
|
3卷引用:北京市昌平区第一中学2023-2024学年高二上学期期中考试数学试题
2 . 已知
,
,
为空间两两垂直的单位向量,且
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9979c9be755ac4fe5ba3a72850df7f9c.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc2ce7e7b90c9a4975d3d69ca98c9b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d52501977a0c7f823c7853a7e33024a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce06860ef7c66ff4d27430fd421b2d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14bec822b8ecab0c51cfe60728eaacc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1e5f6ea4ed889523e3c6e2ffdb4ca95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9979c9be755ac4fe5ba3a72850df7f9c.png)
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名校
解题方法
3 . 若异面直线
的方向向量分别是
,
,则异面直线
与
的夹角的余弦值等于 _____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b270384ef6e4041b44aa962a788657fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/344108836ea6a0a9ba1d22b0f5c66e3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96959387ab866c4ca7c539e57814a3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5d27c081879b6c6bc0abb0ceedb9d3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e5c154445ca71ee9d4fb29a98b8965d.png)
您最近一年使用:0次
2024-03-20更新
|
121次组卷
|
2卷引用:北京市首都师范大学附属中学2022-2023学年高二上学期10月月考数学试题
名校
4 . 已知长方体
的底面
是正方形,
,
,
为棱
的中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deab75d571b23f40cd7b4157f002fa5c.png)
________ .
![](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/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/deab75d571b23f40cd7b4157f002fa5c.png)
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2023-10-22更新
|
137次组卷
|
2卷引用:北京师范大学良乡附属中学2023-2024学年高二上学期10月月考数学试题
名校
5 . 已知空间向量
,
,则向量
在向量
上的投影向量的模是___________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e14e6ce38d3aa1cf65e5ae2ec9eb157e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0caf6edfa3e0dbca0de9ec7d79c230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
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2023-09-15更新
|
959次组卷
|
6卷引用:北京市日坛中学2023-2024学年高二上学期10月月考数学试题
北京市日坛中学2023-2024学年高二上学期10月月考数学试题黑龙江省齐齐哈尔市恒昌中学校2022-2023学年高二上学期期末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月联考数学试题广东省清远市阳山县南阳中学2023-2024学年高二上学期10月月考数学试题辽宁省大连市第八中学2023-2024学年高二上学期10月月考数学试题(已下线)专题01 空间向量与空间位置关系【考题猜想】-2023-2024学年高二数学上学期期中考点大串讲(人教A版2019选择性必修第一册)
6 . 在长方体
中,设
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85f2faa9392b8b7365645f7c89092de.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d64fc81c857b124268609a8beb77b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a85f2faa9392b8b7365645f7c89092de.png)
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7 . 如图,长方体中,
,
,点P为线段
上一点,则
的最小值为
您最近一年使用:0次
8 . 在四面体
中,所有棱长都是1,
,
分别为棱
,
的中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6e239ca7ba34a14dd68c4769220f52.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6e239ca7ba34a14dd68c4769220f52.png)
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名校
解题方法
9 . 在棱长为2的正方体
中,P是棱
上一动点,点O是面AC的中心,则
的值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b6b68b81a05f9f6a53235cc2ef0d16c.png)
您最近一年使用:0次
2022-11-12更新
|
237次组卷
|
3卷引用:北京市顺义区第二中学2022-2023学年高二上学期期中考试数学试题
名校
10 . 如图,在四面体
中,
是
的重心,G是
上的一点,且
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
___________ ;若四面体
是棱长为2的正四面体,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc083b2b91157ca9db6556af68fd2b5.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/011ae6cb0cf49f6d3d19b485dc1cfc22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f9049f32b8b36ebcd94ef69b48d908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4592a7e5f85100f6cd8de62f2ba53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/933cf4d91008779cec543cc771fd9593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee477d164d38ff067fc4ce342cf6d380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4278c0911e7df78965e78cff69cac5f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cc083b2b91157ca9db6556af68fd2b5.png)
![](https://img.xkw.com/dksih/QBM/2022/11/7/3104296360730624/3105082097639424/STEM/90863a7ce44b452c852e299d059c4036.png?resizew=215)
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2022-11-08更新
|
297次组卷
|
3卷引用:北京市朝阳区清华大学附属中学朝阳学校2022-2023学年高二上学期期中考试数学试题