名校
1 . 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
2 . 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
3 . 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
|
1266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
4 . 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
5 . 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
6 . 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)
您最近一年使用:0次
2020-03-10更新
|
465次组卷
|
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
名校
7 . 如图,在多面体
中,
两两垂直,四边形
是边长为2的正方形,AC
DG
EF,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/09519bd8-4db8-427a-8d07-136acd7cf5ad.png?resizew=188)
(1)证明:
平面
.
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1e1ab067de809e8ab8880ef20eef21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83680a9b9a9526f75e0b37aa532132f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d70676406f26d339465fe3473c0c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb31ef428bd9de9bc875b343feded3c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ce38cc648118a6b00041384644f627.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/09519bd8-4db8-427a-8d07-136acd7cf5ad.png?resizew=188)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac0b72906641ed13716cfbce50923282.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb10d645970e5860afd3430957fab6c.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47342449ca1a78a7550975a7589003c5.png)
您最近一年使用:0次
2020-04-24更新
|
229次组卷
|
5卷引用:甘肃省西北师大附中2020届高三5月模拟试卷理科数学试题
名校
8 . 如图,在直三棱柱
中,
是等腰直角三角形,
,
,点D是侧棱
上的一点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/19022026-f43c-4e93-ab78-615a2dc1fa64.png?resizew=120)
(1)证明:当点D是
的中点时,
平面BCD;
(2)若二面角
的余弦值为
求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7ad3a578f403b9e6b97fa2dc955fc11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92535536bd3c2761724fd058427f95a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/19022026-f43c-4e93-ab78-615a2dc1fa64.png?resizew=120)
(1)证明:当点D是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d06903252260d31d1a9cdeb735b089.png)
(2)若二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ceb31247add8ca7b0853e801e1d125.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fac5b7d85cc224776e36a76a4db5d356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b24cbc5c871b748238867c34ffac6f70.png)
您最近一年使用:0次
名校
解题方法
9 . 直三棱柱
中,若
,
,则异面直线
与
所成的角为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/fe90703a-c806-493d-aa58-cf10db411d0e.png?resizew=131)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fd8f940b796af67206b3f9dd410a407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b7d857811cbd619f868d951aa7a0ab8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/fe90703a-c806-493d-aa58-cf10db411d0e.png?resizew=131)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-18更新
|
251次组卷
|
3卷引用:甘肃省兰州市第六十一中学2022-2023学年高三上学期期中数学(文科)试题
名校
解题方法
10 . 如图,在四边形ABED中,AB
DE,AB⊥BE,点C在AB上,且AB⊥CD,AC=BC=CD=2,现将△ACD沿CD折起,使点A到达点P的位置,且PE与平面PBC所成的角为45°.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/537fe6f3-5dd9-410b-867a-204057b21384.png?resizew=180)
(1)求证:平面PBC⊥平面DEBC;
(2)求二面角D-PE-B的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67be899bc131ec1b9921ae9787c40d5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/537fe6f3-5dd9-410b-867a-204057b21384.png?resizew=180)
(1)求证:平面PBC⊥平面DEBC;
(2)求二面角D-PE-B的余弦值.
您最近一年使用:0次