1 . 已知四棱锥
的底面ABCD是边长为2的菱形,且
,
,
,E为PB中点.
![](https://img.xkw.com/dksih/QBM/2023/6/27/3268837724741632/3269523867172864/STEM/f5a9942d32d1418ea60ad54777b58e08.png?resizew=217)
(1)证明:
;
(2)若PB与底面ABCD所成角的正弦值为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bbaccd578a43b2397c8bdd50592fa07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cb96e0331eebe80ed1ff610faf531fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15eae3c2cb4274a947f6a011960934d.png)
![](https://img.xkw.com/dksih/QBM/2023/6/27/3268837724741632/3269523867172864/STEM/f5a9942d32d1418ea60ad54777b58e08.png?resizew=217)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b757706eee506a078fc25e3f33a70cb.png)
(2)若PB与底面ABCD所成角的正弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/502f49e759b623b5c3a8b901bb9882cc.png)
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2 . 在正方体
中,点
是线段
上一动点,则下列各选项正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/2b32d92c-e0f9-44e9-81c5-e6b1e5356f1a.png?resizew=173)
A.![]() |
B.![]() ![]() |
C. 三棱锥![]() |
D.直线![]() ![]() ![]() |
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解题方法
3 . 如图,在四棱锥P—ABCD中,底面ABCD为矩形,侧棱
底面ABCD,
,
,
,E为PD的中点.
(2)在侧棱PAB内找一点N,使
面PAC,并求出N点到AB和AP的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b40d0d2f3cdd8981bb792ad87efb42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
(2)在侧棱PAB内找一点N,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c7f7ffbb802aef097bbe1a9321691f.png)
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4 . 如图,在棱长为2的正方体
中,
,
,
,
,
均为所在棱的中点,则下列结论正确的是( )
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/26/5bd39d5b-13d2-4965-8fb0-8f3d167e89c8.png?resizew=160)
A.棱![]() ![]() ![]() |
B.设点![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.过点![]() ![]() ![]() ![]() |
D.三棱锥![]() ![]() |
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5 . 已知四棱锥P-ABCD中,PA⊥底面ABCD,
,AD=CD=1,∠BAD=120°,
,∠ACB=90°.
(1)求证:BC⊥平面PAC;
(2)求直线PC与平面PAB所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a11029ca6b4b9e7f777af0280cf163c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd3eb538f36e6e722e4ce125266b99b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/20/244ed6eb-17d8-49af-8ce7-6c123f576b9e.png?resizew=160)
(1)求证:BC⊥平面PAC;
(2)求直线PC与平面PAB所成的角的正弦值.
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解题方法
6 . 已知直三棱柱
中,AB
BC,
,D是AC的中点,O为
的中点.点P是
上的动点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6ff6a807f5639faac835012b3728c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/19/c9155ac2-a702-474e-bdc7-e6eff2e098db.png?resizew=180)
A.点P在![]() ![]() |
B.当点P运动到![]() ![]() ![]() ![]() |
C.无论点P在![]() ![]() |
D.当点P运动到![]() ![]() ![]() ![]() |
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7 . 已知直三棱柱
中,
,
,
是
的中点,
为
的中点.点
是
上的动点,则下列说法正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/22/ba06e031-02e9-485f-8708-c0e9aac3d2f0.png?resizew=160)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6ff6a807f5639faac835012b3728c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/22/ba06e031-02e9-485f-8708-c0e9aac3d2f0.png?resizew=160)
A.当点![]() ![]() ![]() ![]() ![]() |
B.无论点![]() ![]() ![]() |
C.当点![]() ![]() ![]() ![]() ![]() ![]() |
D.无论点![]() ![]() ![]() ![]() ![]() |
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四川省内江市第六中学2023-2024学年高二上学期第二次月考数学试题广西南宁市第三中学2021-2022学年高一下学期期中考试数学试题(已下线)第二章 立体几何中的计算 专题一 空间角 微点4 直线与平面所成角【培优版】
名校
解题方法
8 . 从①
,②
平面PAB这两个条件中选一个,补充在下面问题中,并完成解答.
如图,在四棱锥
中,
平面ABCD,
,
,
,______.
(2)求直线PB与平面PCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aa1162d5481e2441fe5bc0d49a576b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6785c7c85a503531649f9c9b4cbfcf04.png)
如图,在四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e921f46d90e43f4517c55832b6280f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be41b05e11ba5eadaaed9a224b949774.png)
(2)求直线PB与平面PCD所成角的正弦值.
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四川省成都市成都市第七中学2022-2023学年高一下学期6月月考数学试题2023版 湘教版(2019) 必修第二册 过关斩将 第4章 4.3 直线与直线、直线与平面的位置关系 4.3.2 空间中直线与平面的位置关系 第2课时 直线与平面垂直(已下线)8.6.1直线与直线垂直+8.6.2直线与平面垂直——课后作业(巩固版)
9 . 已知正方体
的棱长为1,点
为线段
上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
A.![]() ![]() |
B.![]() ![]() |
C.直线![]() ![]() ![]() ![]() ![]() ![]() |
D.点![]() ![]() ![]() ![]() ![]() ![]() |
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10 . 如图,在正三棱柱
中,点
,
分别是棱
,
的中点,连接
,
,
,点
是线段
的中点,点
是线段
上靠近点
的四等分点,则下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db54223bb3fc2fe2497213a4d1f94827.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/3/270c0f35-5ebb-4473-9f18-e2573c43a853.png?resizew=200)
A.平面![]() ![]() |
B.三棱锥![]() ![]() ![]() |
C.直线![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() ![]() ![]() |
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