名校
解题方法
1 . 如图在四棱锥
中,底面
为矩形,
底面
,
是
上一点,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/c458f9b3-d3c6-4f67-801d-e18cd4d17502.png?resizew=189)
(1)求二面角
的大小;
(2)求点
到平面
的距离.
![](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/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbe7a201432af0a2f9d21c6803906f5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66657ffdb8fd7a8ef2f4ac3579437130.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/545d1d96452b302e31d0ff3b31baf23c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/c458f9b3-d3c6-4f67-801d-e18cd4d17502.png?resizew=189)
(1)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b0dc4f92cba842f44477bc9811065c.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf12905647aeeded72bbca21a63f319.png)
您最近一年使用:0次
2020-11-29更新
|
740次组卷
|
9卷引用:甘肃省兰州市教育局第四片区2021-2022学年高二下学期期中考试数学(理)试题
甘肃省兰州市教育局第四片区2021-2022学年高二下学期期中考试数学(理)试题山东省滨州市博兴县第三中学2020-2021学年高二上学期第一次月考数学试题福建省莆田第一中学2020-2021学年高二上学期期中考试数学试题北师大版(2019) 选修第一册 必杀技 第三章 专题3 空间向量的综合应用人教B版(2019) 选修第一册 过关检测 第一章 1.2.5 空间中的距离黑龙江省鸡西市鸡东县第二中学2021-2022学年高二上学期期中数学试题河南省焦作市温县第一高级中学2021-2022学年高二下学期6月月考文科数学试题吉林省白城市通榆县白城市通榆县毓才高级中学有限责任公司2022-2023学年高二上学期期中数学试题湖北省黄冈市黄州中学(黄冈市外国语学校)2023-2024学年高二上学期第一次阶段性测试数学试题
名校
解题方法
2 . 在正方体
中,点E是线段
的中点,则直线
与
所成角的余弦值是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e75d14708e6aa1404477db9d7e3166f0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/5/afda685a-7651-4afb-8e6a-54ac3f571570.png?resizew=174)
您最近一年使用:0次
2020-09-20更新
|
332次组卷
|
5卷引用:甘肃省兰州市教育局第四片区2021-2022学年高二下学期期中考试数学(理)试题
甘肃省兰州市教育局第四片区2021-2022学年高二下学期期中考试数学(理)试题安徽省阜阳市太和中学2019-2020学年高二下学期开学考试数学(理)试题(已下线)专题8.7 立体几何中的向量方法(精练)-2021年新高考数学一轮复习学与练江西省高安中学2020-2021学年高二上学期期末考试数学(理)试题江西省新余市2020-2021学年高二下学期期末数学(理)试题
名校
3 . 如图,已知三棱柱
中,平面
平面ABC,
,
.
![](https://img.xkw.com/dksih/QBM/2020/7/9/2502377418481664/2504067813048320/STEM/87d920da95854bd1a8341b8cc0f194ce.png?resizew=178)
(1)证明:
;
(2)设
,
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46fe926770d2354e172dec02f5ce2efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/615fc8790237a1b09af51d6bcad6b595.png)
![](https://img.xkw.com/dksih/QBM/2020/7/9/2502377418481664/2504067813048320/STEM/87d920da95854bd1a8341b8cc0f194ce.png?resizew=178)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47af45fbf1714055d9b414a44a8613fa.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a8c563906d6d25078fd5d96abe96194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e3c9e7c05de9838c0c5d762720d3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e718d2042232538370f5168f7eb9a1.png)
您最近一年使用:0次
名校
解题方法
4 . 如图,三棱锥
中,
,A、D分别为
、
的中点,
,
,平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/af55e85b-d761-4190-b242-56d09d00b896.png?resizew=153)
(1)证明:
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84160ab4c7e760ae3a09d1cce623a49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef95ebb3e3e81f72c609203f0a046a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e04cc7a52c3ad292d937bfa4507343e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30d502002ad65d8bc45f71693fb79256.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f464948420e7b666335bfd60f7678e7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/25/af55e85b-d761-4190-b242-56d09d00b896.png?resizew=153)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d71b7cbc7958bc5a520aad74842e59e8.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3336e307c79e059770bf1a46d2974df7.png)
您最近一年使用:0次
名校
5 . 如图,在三棱柱
中,
平面
,
,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/1086a6ac-8473-4a59-a0a7-82ab95af2f97.png?resizew=164)
(1)证明:
平面ABC.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56fdf217165748fafe938b64fa08179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca036d049f5205cf04cb1b9c5cd03f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f656e1d1f68954e5f06de8958f6a9310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/518a322494bd7624e6eed7fe290a2f9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/14/1086a6ac-8473-4a59-a0a7-82ab95af2f97.png?resizew=164)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e89195bacd53d43195e70c12b5cfa041.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a824c242050a27d9da3bb3276ea99170.png)
您最近一年使用:0次
2020-07-11更新
|
430次组卷
|
4卷引用:甘肃省兰州外国语高级中学2021-2022学年高三上学期第一次适应性考试数学(理科)试题
名校
6 . 如图,在四棱锥
中,
为平行四边形,
,
平面
,且
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/97c57169-77b2-45fc-93b1-d98687a06cec.png?resizew=236)
(1)求证:
平面
;
(2)在线段
上(不含端点)是否存在一点
,使得二面角
的余弦值为
?若存在,确定
的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf01adbdbab49dc9915b957ddf85351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.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/1bb7b50091ad217f18db44fe0fc1550a.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/2022/11/2/97c57169-77b2-45fc-93b1-d98687a06cec.png?resizew=236)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46e2da608b66c9aee03e2503388ba4fd.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e4cb797a03b0d96fa146543101f993c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-05-21更新
|
712次组卷
|
8卷引用:甘肃省兰州市外国语高级中学2022届高三上学期9月建标考试理科数学试题
名校
解题方法
7 . 已知,图中直棱柱
的底面是菱形,其中
.又点
分别在棱
上运动,且满足:
,
.
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453970522234880/2453997798014976/STEM/4358c504-ca50-4dc5-b48b-a8ee2b0667d6.png)
(1)求证:
四点共面,并证明
∥平面
.
(2)是否存在点
使得二面角
的余弦值为
?如果存在,求出
的长;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffa102f519d541f2e4d10a8975a41c36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/360a93b9662f0ab8a69b131497520b53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626db48efbecf4e318252ba13baff47d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1357d24d53b523a55b3eea7b21fa16f1.png)
![](https://img.xkw.com/dksih/QBM/2020/5/2/2453970522234880/2453997798014976/STEM/4358c504-ca50-4dc5-b48b-a8ee2b0667d6.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d6dc34b0b71d46a91eb8dd8db01f5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c51c4a1148587943fe9ba210f6141ee.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e807172fa9eca2416f92f341adc06165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dee14db57f0c762aad845cf5b4a243c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
您最近一年使用:0次
2020-05-02更新
|
1267次组卷
|
5卷引用:甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(理)试题
甘肃省兰州市第一中学2020届高三冲刺模拟考试(三)数学(理)试题2020届河南省高三第十次调研考试数学(理)试题江西省分宜中学、玉山一中等九校2019-2020学年高三联合考试数学理科试卷河北省衡水中学2019-2020学年高三下学期第十次调研数学(理)试题(已下线)1.4 空间向量的应用-2021-2022学年高二数学尖子生同步培优题典(人教A版2019选择性必修第一册)
2020高三·全国·专题练习
解题方法
8 . 已知圆锥的顶点为A,高和底面的半径相等,BE是底面圆的一条直径,点D为底面圆周上的一点,且∠ABD=60°,则异面直线AB与DE所成角的正弦值为( )
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-04-30更新
|
240次组卷
|
3卷引用:2020届甘肃省兰州市高三诊断考试数学(理)试题
9 . 如图,在四棱锥
中,
底面
,底面
为直角梯形,
,
∥
,
,
,
,
,
分别为线段
,
,
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/5ccd7d30-af51-43da-bed5-21fe47655d8b.png?resizew=224)
(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/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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a77d517bf9621d8e491eceecfcd0ed7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.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/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/5ccd7d30-af51-43da-bed5-21fe47655d8b.png?resizew=224)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d246f9eceab371ebf47a47c2f11a4ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b1980f7a8ddeab4265002aa9fdb6920.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8e5f736b1195fef1d2d300168a795f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
您最近一年使用:0次
2020-04-24更新
|
523次组卷
|
5卷引用:甘肃省兰大附中2020届高三5月月考数学(理科)试题
甘肃省兰大附中2020届高三5月月考数学(理科)试题2020届全国100所名校最新高考模拟示范卷高三模拟测试理科数学(二)2020届全国100所名校最新高考模拟示范卷高三理科数学模拟测试试题(二)(已下线)1.4.2 空间向量的应用(二)(精练)-2020-2021学年一隅三反系列之高二数学新教材选择性必修第一册(人教版A版)安徽省蚌埠第三中学2021-2022学年高二上学期10月教学质量检测数学试题
名校
解题方法
10 . 如图,在四棱锥
中,
底面ABCD,底面ABCD为梯形,
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a92932d5-fbb2-4d32-9c31-393b372e8196.png?resizew=168)
(1)在PD上是否存在一点F,使得
平面PAB,若存在,找出F的位置,若不存在,请说明理由;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0facf189b2a3153beb7b9e077d3b1146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34a86542e55ad35b90a5c7afd23e8803.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a92932d5-fbb2-4d32-9c31-393b372e8196.png?resizew=168)
(1)在PD上是否存在一点F,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350d224711c8773a7c5a2b34bf40bedc.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2425afeae790f548529e24c81a40560c.png)
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2020-03-10更新
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465次组卷
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3卷引用:2020届甘肃省兰州市第二中学高三第五次月考理科数学试题