1 . 如图,在平行六面体
中,
平面
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/e0bb10cc-07f5-4c60-95df-48e535cec68f.png?resizew=171)
(1)求证:
;
(2)线段
上是否存在点
,使得平面
与平面
的夹角为
?若存在,求
的长;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ddbb0422a136f45653c8c369f2d75fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4615b646e7f1d30265d3fdd4f8439fe3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f02723217767fbe9da511292d1be7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83472c2139c75eea390cfc0e1104e296.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/e0bb10cc-07f5-4c60-95df-48e535cec68f.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbeb1554fc1cec56b983a08e9dc52c85.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65277734669566578cbb7d690bb200fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
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2 . 在平行六面体
中,
为
延长线上一点,且
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb69ae7bc9b325bd8d128a78fb2dcaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/837755b76f7baa821e707ac519d05b2b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 在四棱锥
中,底面
为平行四边形,点
满足
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c309a8fefe5005f98d8d4cc9c54ab7c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/658ff9921ff96972b0fc95360bb0c65b.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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4 . 下列给出的命题正确的是( )
A.若![]() ![]() |
B.点![]() ![]() ![]() ![]() |
C.若直线![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.两个不重合的平面![]() ![]() ![]() |
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5 . 已知三棱锥
,点
是棱
的中点,点
是
的重心,设
,
,
,则下列向量中与
相等的向量是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fbe26300948274d3de53de77ac3d82c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f3e48ef4edc34b13c4431edb3dee7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f71c08c5ce959677462ef156c6699f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a014dff8997c661055229de29c61cfc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/9dd146e2-32b7-4ef2-bf78-0a178f29aaf5.png?resizew=159)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 如图,在四面体
中,
,
,且
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/a31b9b3e-7098-4772-a1f6-ecadce52e283.png?resizew=159)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc5343d0ed7b449971c7ba787a621fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbbfde69bc71a2202ad20e512337e225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d627b9a5b268fe69aa466f7c465c5f3f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/18/a31b9b3e-7098-4772-a1f6-ecadce52e283.png?resizew=159)
A.![]() | B.![]() |
C.![]() | D.![]() |
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7 . 在棱长为2的正四面体A-BCD中,E,F分别是AD,BC的中点,G是△BCD的重心,则下列结论正确的是( )
A.![]() | B.![]() |
C.![]() ![]() ![]() | D.![]() |
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2024-02-14更新
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2卷引用:福建省宁德市古田县第一中学2023-2024学年高二下学期第一次月考数学试卷
名校
8 . 已知
,
,
三点共线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e0a03cc379d2886092fed4bdea32d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b1be0481a8f25799d35d7cecf133d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f91155d51ae9043aa00bd064bb03cd50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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4卷引用:福建省厦门市2023-2024学年高二上学期1月期末质量检测数学试题
福建省厦门市2023-2024学年高二上学期1月期末质量检测数学试题(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)江苏省射阳中学2023-2024学年高二下学期3月阶段测试数学试题(已下线)模块四 期中重组卷4(江苏苏北五市)(苏教版)(高二)
解题方法
9 . 已知梯形
中,
,
,
,
,
.如图,将
沿对角线
翻折至
,使得
,则异面直线
,
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1229ba36a93222692bf76be9695bf5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/714cc3707bba3bfdb56e251999be8592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e2a44d05b1d387150c4b359e021ffc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ea25ef38e4afa8f75ffd0842890289.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf620ceea251b79d97d3e96273788afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e663220a66eff19da6a71e46b397db2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/21/331bfc93-16b5-472d-b900-b8dd8f77ad28.png?resizew=170)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:福建省厦门市2023-2024学年高二上学期1月期末质量检测数学试题
福建省厦门市2023-2024学年高二上学期1月期末质量检测数学试题四川省绵阳市江油市太白中学2023-2024学年高二下学期开学考试数学试题(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点1 翻折、旋转中的基本问题(一)(已下线)第三章 折叠、旋转与展开 专题一 平面图形的翻折、旋转 微点8 平面图形的翻折、旋转综合训练
名校
10 . 如图,空间四边形
中,
,点
在
上,且
,点
为
中点,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/dbc95f97-2ec0-4bfa-96db-660a6b40621f.png?resizew=150)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddc5343d0ed7b449971c7ba787a621fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe72d1b634f1e89d8699e605e7d46af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8926ddd0b69d714c7310cc5bf23d199d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/12/dbc95f97-2ec0-4bfa-96db-660a6b40621f.png?resizew=150)
A.![]() | B.![]() |
C.![]() | D.![]() |
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