1 . 如图,已知斜三棱柱
的侧面
是菱形,
,
.
;
(2)求平面
与平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c853c91c054b7e1cd0de891aeedc8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ae571b7fbebf3f266bb955dac2c572e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd06851d747f8ccf046bc807b2523e65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d3f9e8e58175cc46453515621e69193.png)
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解题方法
2 . 在空间直角坐标系中,已知A(0,6,4),B(0,3,4),C(4,3,4),
(0,6,0),
(0,0,0),
(8,0,0),则几何体
的体积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
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3 . 如图,四棱锥
的底面为矩形,平面
平面
是边长为2的等边三角形,
,点
为
的中点,点
为线段
上一点(与点
不重合).
;
(2)当
为何值时,直线
与平面
所成的角最大?
(3)在(2)的条件下,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/342d452a7b850cd3a15b23619ad39bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3826f38ba13d3cdac1485ac3b67bc1de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f144992e1cbee34868abce1e5ad38c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e6e0bfb13d3403be93723a9915c07a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ab924e3692515bd8be4c36472a959a.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
(3)在(2)的条件下,求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
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解题方法
4 . 在四棱锥
中,底面
是边长为3的正方形,
底面
,点
在侧棱
上,且满足
,则异面直线
和
的距离为( )
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7992a6b8d2458fca5dbe44c4320e9b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cda041848f97502ffc755f1ce484f92c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e72b2e1ff83e95df048745322982451.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-05-08更新
|
462次组卷
|
4卷引用:江苏省靖江高级中学2023-2024学年高二下学期期中考试数学试题
江苏省靖江高级中学2023-2024学年高二下学期期中考试数学试题江苏省淮安市洪泽中学,金湖中学,清河中学,清浦中学等学校2023-2024学年高二下学期5月月考数学试题(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)甘肃省兰州第一中学2023-2024学年高二下学期5月月考数学试题
名校
解题方法
5 . 如图,在三棱柱
中,底面
是以
为斜边的等腰直角三角形,侧面
为菱形,点
在底面上的投影为
的中点
,且
.
;
(2)求点
到侧面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a382ccd078374f1efebb26a43599e596.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
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解题方法
6 . 如图,平行六面体
的底面是菱形,且
,
,
.
(1)求
的长;
(2)求异面直线
与
所成的角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a6ee51af9b52152488b1772fa190fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037b342a682cbd4241855a243da3c016.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c122ca7141c43c15c783968f5f0dbc19.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/7/c687cbff-7aa4-424d-b71e-4039e2188c3b.png?resizew=201)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabe764f05300ac83c7d16b685d27af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
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解题方法
7 . 如图,在直三棱柱
中,
,
,M是
的中点,以C为坐标原点,建立如图所示的空间直角坐标系.若
,则异面直线CM与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3cc9cccfb4c260dac05f4ed57e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2213206b187a69e5e298f770b054ccce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed7988dc0ec37adbc0162ac19933ac4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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8 . 如图,在棱长为1的正方体
中,点
分别是棱
的中点,则异面直线
与
所成角的正弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f650481726f091d693138126453e050.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/167d31eb8432b5c0364316e5048c23dd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-04-05更新
|
157次组卷
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5卷引用:江苏省连云港市灌南县惠泽高级中学2023-2024学年高二下学期第一次月考数学试题
江苏省连云港市灌南县惠泽高级中学2023-2024学年高二下学期第一次月考数学试题(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)吉林省四校2023-2024学年高二下学期期初联考数学试题福建省莆田第四中学2023-2024学年高二下学期第一次月考数学试卷
名校
解题方法
9 . 抛物线
的焦点为
,对称轴为
,过
且与
的夹角为
的直线交
于
两点,
的中点为
,线段
的中垂线MD交
于点
.若
的面积等于
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7a3159579864a8ea0ab42005144864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1189b88e124cb3e33c799a073d60ca73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
A.4 | B.![]() | C.2 | D.![]() |
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解题方法
10 . 如图,在正四棱柱
中,
,
,E为
的中点,经过BE的截面与棱
,
分别交于点F,G,直线BG与EF不平行.
共点;
(2)当
时,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cfd898d33c71be3c212277d9e4da2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0acbd5d35287047b8ff024d00a3eaec0.png)
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