解题方法
1 . 如图,在正四棱柱
中,底面边长为2,高为4.
(1)证明:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/7/3ec0d458-e22b-414d-8b06-f34d76c2d2ca.png?resizew=120)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0db5b8d1bf3bee0237d7c50c9cda64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc78a86b12ba0b4553135a3a635fc418.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da7977ab975efa6411cc17de39be70d9.png)
您最近一年使用:0次
解题方法
2 . 如图,在平面四边形
中,
为
的中点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8fe04ea10416809db115e743eb1468d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
,且
.将此平面四边形
沿
折成直二面角
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/29dc8048-763a-48ab-a847-db01a9b88369.png?resizew=295)
(1)证明:平面
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b027ed57b9c6f24e27ec0ae282c76efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8fe04ea10416809db115e743eb1468d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4654c3481f78f939c3267b42d57262d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b027ed57b9c6f24e27ec0ae282c76efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35471e5a1da79efc952ff6aa905616f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f8cd87144a823ca72d3917ffe55006.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/4/29dc8048-763a-48ab-a847-db01a9b88369.png?resizew=295)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04c222223dae9ef27d4c132534d9848.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
3 . 如图,在四棱锥
中,四边形ABCD是边长为2的正方形,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/b952af2e-3e5a-4ed8-82c2-e18c55c46756.png?resizew=131)
(1)证明:平面
平面
;
(2)若
,
,点E,F分别为PB,PD的中点,求点E到平面ACF的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d02bd5cfe804460846423e77f72db10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d0710321d97361e5782124bbf7f0c9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/1/b952af2e-3e5a-4ed8-82c2-e18c55c46756.png?resizew=131)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f571a1aac46c6d0cf440c0ec2846bf9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af2c4b7601274731a0f8140c99762501.png)
您最近一年使用:0次
解题方法
4 . 如图,在四棱锥
中,底面ABCD为平行四边形,
为等边三角形,
,
,
,点E满足
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/79724376-1af7-4662-87f1-a44e656b276a.png?resizew=162)
(1)证明:平面
平面ABCD;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d58da37b3d1dbd2fee75089d5ba28134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f44bec66934dd2d35ffbf7d863892ed.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/79724376-1af7-4662-87f1-a44e656b276a.png?resizew=162)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
您最近一年使用:0次
名校
解题方法
5 . 在三棱台
中,
底面
,底面
是边长为2的等边三角形,且
,D为
的中点.
平面
.
(2)平面
与平面
的夹角能否为
?若能,求出
的值;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ecf072589c0f901d92f6bda111d841.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/787ac5e13622afab5e9f8603afe42356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c0a06a56ad5be6b3773c48daa7f7e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69771fbcfc8f07cfb7ece1d2c2e6830b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
(2)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9b7b7793d29d66dfdd89e7a6564a35c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f96c673a2381f118ea2d3efc0bca1f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
您最近一年使用:0次
2024-01-24更新
|
224次组卷
|
3卷引用:广东省肇庆市2023-2024学年高二上学期期末教学质量检测数学试题
名校
解题方法
6 . 如图,在棱长为
的正方体
中,点
是正方体的中心,将四棱锥
绕直线
逆时针旋转
后,得到四棱锥
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/70eaf1d9-40ba-4fe0-a96f-0af246dc88a1.png?resizew=269)
(1)若
,求证:平面
平面
;
(2)是否存在
,使得直线
平面
,若存在,求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9a0c3a4e61b97fa9bc58f3179fc2958.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debc6eb7acc1f38ef267ce976bc08891.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa19f78fd19c8e5601bba0f52e438ca6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a72df364fb19388f4a9f691fb04e6851.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/70eaf1d9-40ba-4fe0-a96f-0af246dc88a1.png?resizew=269)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1676b17f3641daf630f709517d22d120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e238b13232095d5859e5a622d09233d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/715c368ff97dfe2f168c15bc6a3fe9a3.png)
(2)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f3fdee3ca530bf2fe6583112972e63a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2730b513bd3359c3dfe6567e04f5ef9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2024-01-24更新
|
2016次组卷
|
4卷引用:广东省华附 深中 省实 广雅四校联考2024届高三上学期期末数学试题
广东省华附 深中 省实 广雅四校联考2024届高三上学期期末数学试题(已下线)最新模拟重组精华卷2 -模块一 各地期末考试精选汇编湖南省长沙市雅礼中学2024届高三下学期3月综合测试(一)数学试题(已下线)第七章 应用空间向量解立体几何问题拓展 专题二 平面法向量求法及其应用 微点1 平面法向量求法及其应用(一)【培优版】
7 . 如图1,在矩形ABCD中,
,
.将△BCD沿BD翻折至
,且
,如图2.
平面
;
(2)求平面
与平面ABD夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d021334737f555d75a65177f7ebebc81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed1efb2224920c1769400e7222006347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/140088b0cb73812aa9d523c44559298a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a935b7d21a103a264b6e96ecf82dbe4a.png)
您最近一年使用:0次
23-24高三上·湖北十堰·期末
解题方法
8 . 正三棱柱
中,
,
,
,
分别为
,
,
的中点,
为棱
上的动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
A.平面![]() ![]() |
B.点![]() ![]() ![]() |
C.![]() ![]() ![]() |
D.以![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
9 . 如图所示,四边形ABCD为圆柱ST的轴截面,点Р为圆弧BC上一点(点P异于B,C).
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
,
(
),且二面角
的余弦值为
,求
的值.
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8798f21caf1819d47db778d23fa57b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2590902f4edd2fa6b233ef54a31862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d80c787eefc6da2a49d25d2caeaa5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-12更新
|
1137次组卷
|
5卷引用:广东省梅州市梅县东山中学2024届高三上学期期末数学试题
2024·全国·模拟预测
10 . 在三棱锥
中,已知
,棱AC,BC,AD的中点分别是E,F,G,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b13d28cb7181257cf732af4b615fc47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2539dc18fc736983e69dcc4a2b2f93.png)
A.过点![]() |
B.平面![]() ![]() |
C.异面直线![]() |
D.三棱锥![]() ![]() |
您最近一年使用:0次