名校
解题方法
1 . 《九章算术》把底面为直角三角形,且侧棱垂直于底面的三棱柱称为“堑堵”,现有如图所示的“堑绪”
,其中
,
,若“堑绪”
的体积为
,则“堑堵”
的外接球的表面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd108abaf2b7fc1d0239b28afcf4ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a44d321ae2abfc4e566933a92637d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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2 . 如图,在四棱锥
中,底面
是平行四边形,
,若
,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/4b54509386a3872c629f0ed9e92d1bc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881491c15de67028d540787b2a252063.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/3/a779dce3-9950-41f2-a5c7-6b92e25a7be4.png?resizew=178)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 已知空间向量
,若
共面,则实数
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd1858e7979422e390faa10019a1c4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/799ad95449b4135dee2890ac31c43706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
A.0 | B.1 | C.2 | D.3 |
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4 . 如图,在长方体
中,
,M,N分别为棱
,
的中点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/7725b539-e91f-4b10-9e22-8109f415b9cc.png?resizew=159)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2924712990f46497e869ca114504ec7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/7725b539-e91f-4b10-9e22-8109f415b9cc.png?resizew=159)
A.![]() ![]() |
B.![]() ![]() |
C.异面直线![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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5 . 如图,在三棱锥
中,
是
的中点,
是
的中点,点
在线段
上,且
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
平面
;
(2)若
平面
,且
,求直线
与平面
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/276e3c9755dbd39fb01de614840d230f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3ddf544355087a7a42096000db11b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d342cbee09a0cbf04ab7bdccd718b15e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
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5卷引用:辽宁省朝阳市建平县2024届高三上学期期末数学试题
辽宁省朝阳市建平县2024届高三上学期期末数学试题河北省廊坊市部分高中2024届高三上学期期末数学试题(已下线)专题13 空间向量的应用10种常见考法归类(2)广东省广州市仲元中学2024届高三第二次调研数学试题(已下线)专题05 空间向量与立体几何(分层练)(四大题型+21道精选真题)
解题方法
6 . 已知正方体的棱长为2,M为空间中任意一点,且
,当三棱锥
的体积最大时,其外接球的表面积为
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辽宁省朝阳市建平县2024届高三上学期期末数学试题(已下线)第八章 立体几何初步 单元复习提升(易错与拓展)(1)-单元速记·巧练(人教A版2019必修第二册)吉林省白城市通榆县第一中学校2024届高三上学期第五次质量检测数学试题
名校
7 . 已知
,
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbc898591206900808334db44311ec95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf32bf961e6c83464b298b1ba8dc705b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6123f13e3efcf5a6bd142d9fbbe5f84d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-12-31更新
|
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8 . 如图,在四棱锥
中,
,
,
平面
,
,
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/03c73120-6bd7-490e-b2ba-c578741dbcbc.png?resizew=175)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be41b05e11ba5eadaaed9a224b949774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5b0382c28547d3834ca71f3f0677695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37002ada5d194d4d062fa3285d7d9824.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9133fe4c010285dc9f6d02b0fc45461b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba8c7d2b78ab2452b0a57925241dbdb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5745e2dc1d5308872c68ae932cd13ffa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/03c73120-6bd7-490e-b2ba-c578741dbcbc.png?resizew=175)
A.1 | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 已知
,
,
,
,则点
到平面
的距离为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2d977eaaf129783581dcee97f44c96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffdb8b12052e9779cc91977a1043022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54f6825059d3ddcae7167f01bf22917e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39fc2030ca89523b02c2ad5cb9777ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-11-19更新
|
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10 . 如图,在四棱锥
中,底面ABCD是正方形,E是PD的中点,点F满足
,若
,
,
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/28d9c30f-cf97-4eea-8f00-d1cb7afcb3ca.png?resizew=150)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aae6d917ea0c5d5e28003c66281b6759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d9ac737639ad7ce99887f9ef07685c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d20a9410ceb649e303910f8efe5f7531.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbadd77fde781d924b14e6dc57505ccf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fc75903617d7f97f13e47091f956bc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/14/28d9c30f-cf97-4eea-8f00-d1cb7afcb3ca.png?resizew=150)
A.![]() | B.![]() |
C.![]() | D.![]() |
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