名校
1 . 已知四棱柱
中,底面
为菱形,
,
为
中点,
在平面
上的投影
为直线
与
的交点.
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6be7370058c9b0b4dd6fe7d999dfa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d98c843d3cc814335f8d4796bf131d7.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/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df6b00aa8eb26bee3d039144c2c8cfaf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b7330a47ee62725071b8df19e0f748c.png)
您最近一年使用:0次
2020-03-16更新
|
888次组卷
|
3卷引用:江西省景德镇一中2019-2020学年高二上学期期末考试数学试题
名校
解题方法
2 . 如图,在三棱锥
中,平面
平面
,
为等边三角形,
,且
,E,F分别为AC,PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/c686e2c5-6be9-4775-91ee-9d49f55350b7.png?resizew=183)
(1)求证:
平面
;
(2)求证:平面
平面
;
(3)求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfcae2cecc98e2d6c16dde6d3ec1c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4957406b21df59fdf7fa184752287b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/c686e2c5-6be9-4775-91ee-9d49f55350b7.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51838e395dfc9d9ef597d9e01f46272.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
您最近一年使用:0次
名校
解题方法
3 . 在直四棱柱
中,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/ea693263-970e-4cef-9aed-e86a4a706706.png?resizew=108)
(1)证明:
;
(2)求四棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700a29bdea75bb619871ce408933056c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07b9534f197f793b1b88efdf96181bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/2/ea693263-970e-4cef-9aed-e86a4a706706.png?resizew=108)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed026d18604cef1de3aec4cccf5a22f7.png)
(2)求四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4acec58b956dd6307105578aea3c9fd0.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,四棱锥
中,
平面
,底面
是边长为2的正方形,
,
为
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/b6f336f1-5b43-465d-ba2d-9b76fedb885f.png?resizew=157)
(1)求证:
;
(2)求二面角
的正弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/b6f336f1-5b43-465d-ba2d-9b76fedb885f.png?resizew=157)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4486d52b6e410fd7b60428121d96cef.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306681bd5aaa51e9c63ab3002e23dec5.png)
您最近一年使用:0次
2020-02-27更新
|
336次组卷
|
4卷引用:2020届陕西省西安市高三年级第一次质量检测数学理科试题
2020届陕西省西安市高三年级第一次质量检测数学理科试题四川省泸州市泸县第五中学2020-2021学年高三上学期第一次月考数学(理)试题(已下线)专题09 法向量秒求-2021年高考数学二轮复习解题技巧汇总(新高考地区专用)黑龙江省哈尔滨市第三十二中学2020-2021学年高三上学期期末考试理科数学试题
名校
解题方法
5 . 如图,四棱锥
中,
底面ABCD,且底面ABCD为平行四边形,若
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/7f20a2ab-04fa-458d-b3fa-6bde5d9a81c4.png?resizew=170)
(1)求证:
;
(2)若
,求直线PB与平面PCD所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4f5eec0addba78f2e0cdfb7ecc59a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4aca5534bce25acaeb7379deed8f8f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/7f20a2ab-04fa-458d-b3fa-6bde5d9a81c4.png?resizew=170)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b07e317ffe7859e81b42ef4970e344a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/068e62c79ff7a527ff494db199d40b50.png)
您最近一年使用:0次
2020-02-23更新
|
285次组卷
|
3卷引用:安徽省合肥市庐阳区第一中学2019-2020学年高二上学期10月月考数学(理)试题
解题方法
6 . 如图,四棱锥S-ABCD的底面是边长为2的正方形,每条侧棱的长都是底面边长的
倍,P为侧棱SD上的点.
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402332506251264/2403054239825920/STEM/64f91c23cb864fafb95b8ae3dc103fb2.png?resizew=129)
(1)求证:AC⊥SD;
(2)若SD⊥平面PAC,求二面角P-AC-D的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402332506251264/2403054239825920/STEM/64f91c23cb864fafb95b8ae3dc103fb2.png?resizew=129)
(1)求证:AC⊥SD;
(2)若SD⊥平面PAC,求二面角P-AC-D的大小.
您最近一年使用:0次
2020-02-20更新
|
465次组卷
|
2卷引用:湖南省永州市2019-2020学年高一上学期期末数学试题
解题方法
7 . 如图,四棱锥
的底面
是边长为2的菱形,
,
平面
,点
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/14f4f138-02fe-4e7c-87c0-e89287800e0f.png?resizew=205)
(1)证明:
;
(2)当
时,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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/30/14f4f138-02fe-4e7c-87c0-e89287800e0f.png?resizew=205)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4125524caac016727c80d2722c5ba3.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
名校
解题方法
8 . 如图:
平面
,
是矩形,
,
,点
是
的中点,点
在边
上移动.
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402332989947904/2402429698990080/STEM/c74f674ee5f945a9afbe9283603dfbbf.png?resizew=200)
(Ⅰ)求三棱锥
的体积;
(Ⅱ)当点
为
的中点时,试判断
与平面
的位置关系,并说明理由;
(Ⅲ)证明:无论点
在边
的何处,都有
.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7b6d04f024ca05cdfacc8ce9137c15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d783fe7f3ce673d5d21281174e7a7968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/2020/2/19/2402332989947904/2402429698990080/STEM/c74f674ee5f945a9afbe9283603dfbbf.png?resizew=200)
(Ⅰ)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37d1190fdc8609b1e43957aaaaf4abbe.png)
(Ⅱ)当点
![](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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(Ⅲ)证明:无论点
![](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/4a395778dcf588264f40e1cd8c96206d.png)
您最近一年使用:0次
2020-02-19更新
|
425次组卷
|
3卷引用:宁夏银川市六盘山高级中学2019-2020学年高一上学期期末数学试题
名校
解题方法
9 . 如图,在三棱锥
中,
是边长为1的正三角形,
,
.
![](https://img.xkw.com/dksih/QBM/2020/2/13/2398365843947520/2399460610719745/STEM/40cce10b92dc4bab90d2a74bfc1724ac.png?resizew=234)
(1)求证:
;
(2)点
是棱
的中点,点P在底面
内的射影为点
,证明:
平面
;
(3)求直线
和平面
所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c24b7a9466a1e35328a8a4b1ba7fa84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d60df9713216819939438d60fdc3e3f.png)
![](https://img.xkw.com/dksih/QBM/2020/2/13/2398365843947520/2399460610719745/STEM/40cce10b92dc4bab90d2a74bfc1724ac.png?resizew=234)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccbd1316b9d1f0c1e71fd078deec61f6.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e35a6cf772fbe75c29b6c27193b3c9a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
名校
解题方法
10 . 在正方体
中.
![](https://img.xkw.com/dksih/QBM/2020/2/12/2397643038875648/2398229448925184/STEM/15f11493da76443fb5404490140ddda4.png?resizew=198)
(1)求证:
;
(2)
是
中点时,求直线
与面
所成角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://img.xkw.com/dksih/QBM/2020/2/12/2397643038875648/2398229448925184/STEM/15f11493da76443fb5404490140ddda4.png?resizew=198)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f217a2438de689a0476f63e8d8f380c.png)
(2)
![](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/19ef601ca1f9c4c031adab4ffed297f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c33c6587f6e6ec7e400046516bb2c015.png)
您最近一年使用:0次
2020-02-13更新
|
219次组卷
|
2卷引用:黑龙江省哈尔滨市第三中学2018-2019学年高一下学期期末数学试题