解题方法
1 . 如图,在三棱锥
中,平面ABD
平面BCD,
,O为BD的中点,△OCD是边长为2的等边三角形.
(1)若
,求直线AB和CD所成角的余弦值;
(2)若点E在棱AD上,
且三棱锥
的体积为4,求二面角
平面角大小的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/16/e57f8ac7-b773-4a17-bafa-2cfe90375c3c.png?resizew=190)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
(2)若点E在棱AD上,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940099db7ffe6b3f7e70afcfba66750a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324d453870b345da0c41977290192f94.png)
您最近一年使用:0次
解题方法
2 . 如图,在四棱锥
中,DA⊥平面ABE,
,
,
,F是DE的中点.
平面ABE;
(2)若
,直线DE与平面ABE所成角为
,求直线CF与直线DB所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a6f0f2e5bc1f05ed844291b55513da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa7aeb2a8d1437eeb4482c3b6ad9f315.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b547d886c528fa2c63016c217b8fb51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94270844f197d524bf1da4f1385befd2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6164f6484b3b4acafcf1f3fd87ef196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
您最近一年使用:0次
名校
3 . 如图所示,在正三棱柱ABC-A1B1C1中,AB=2,AA1=1,点D是AB的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/a13efed4-83ba-4101-9e3a-c53de9186a5b.png?resizew=154)
(1)求点B到平面B1CD的距离;
(2)求异面直线AC1和B1C所成角的余弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/a13efed4-83ba-4101-9e3a-c53de9186a5b.png?resizew=154)
(1)求点B到平面B1CD的距离;
(2)求异面直线AC1和B1C所成角的余弦值.
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4 . 如图所示,正四棱锥
中,
为底面正方形的中心,已知侧面
与底面
所成的二面角的大小为
,
是
的中点.
(1)请在棱
与
上各找一点
和
,使平面
平面
,作出图形并说明理由;
(2)求异面直线
与
所成角的正切值;
(3)问在棱
上是否存在一点
,使
侧面
,若存在,试确定点
的位置;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(1)请在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02d943ee1f585e766961175ff5950494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(3)问在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a5f445af1ae136773cb338920552ff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2022/7/28/3032184793858048/3032957836271616/STEM/3278e788c4cd482ba4689e7351739f33.png?resizew=181)
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2022-07-29更新
|
885次组卷
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5卷引用:安徽省黄山市2021-2022学年高一下学期期末数学试题
安徽省黄山市2021-2022学年高一下学期期末数学试题安徽省滁州市定远县育才学校2022-2023学年高一下学期期末考试数学试卷(已下线)8.6.3平面与平面垂直(第1课时平面与平面垂直的判定定理)(精讲)(1)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)(已下线)考点巩固卷17 空间中的平行与垂直(八大考点)(已下线)第五章 破解立体几何开放探究问题 专题一 立体几何存在性问题 微点1 立体几何存在性问题的解法(一)【基础版】
5 . 底面是菱形的直四棱柱
中,
,且
,
.
(1)求异面直线
与
所成角的余弦值;
(2)若
为线段
的中点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
(1)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe80a3270ed76c92ab4bdc4bc247e50.png)
您最近一年使用:0次
2022-07-08更新
|
479次组卷
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3卷引用:安徽省蚌埠市2021-2022学年高一下学期期末数学试题
名校
解题方法
6 . 在如图所示的圆锥中,底面直径与母线长均为4,点C是底面直径
所对弧的中点,点D是母线PA的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/7/d61eb725-73b8-4bb4-960e-31f90f7e04c0.png?resizew=150)
(1)求该圆锥的侧面积与体积;
(2)求异面直线AB与CD所成角的正切值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/7/d61eb725-73b8-4bb4-960e-31f90f7e04c0.png?resizew=150)
(1)求该圆锥的侧面积与体积;
(2)求异面直线AB与CD所成角的正切值.
您最近一年使用:0次
2023-04-05更新
|
381次组卷
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4卷引用:安徽省安庆一中2018-2019学年高一第二学期期末考试数学试题
安徽省安庆一中2018-2019学年高一第二学期期末考试数学试题山东省滕州市第一中学2019-2020学年高一4月网课检测数学试题(已下线)第6讲 立体几何小题(2) -《考点·题型·密卷》云南省昭通市绥江县第一中学2020-2021学年高二上学期第一次月考数学试题
名校
7 . 在四面体A-BCD中,E,F,M分别是AB,BC,CD的中点,且BD=AC=2,EM=1.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/76b40c7f-e008-4789-8b5f-d37144406b6f.png?resizew=212)
(1)求证:
平面ACD;
(2)求异面直线AC与BD所成的角.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/8/76b40c7f-e008-4789-8b5f-d37144406b6f.png?resizew=212)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
(2)求异面直线AC与BD所成的角.
您最近一年使用:0次
2022-04-20更新
|
792次组卷
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10卷引用:安徽省安庆市2020-2021学年高一下学期期末数学试题
安徽省安庆市2020-2021学年高一下学期期末数学试题山东省滨州市2019-2020学年高一(下)期末数学试题山东省滨州市2019—2020学年下学期高一年级期末考试数学试题天津市实验中学滨海学校2020-2021学年高一下学期期中数学试题北师大版(2019) 必修第二册 金榜题名 第六章 单元素养评价天津市西青区当城中学2022-2023学年高一下学期期中数学试题四川省威远中学2020-2021学年高二上学期第一次月考数学(理)试题沪教版(2020) 必修第三册 精准辅导 第10章 单元测试四川省遂宁市射洪中学校2022-2023学年高二上学期第一次学月考试数学(文科)试题四川省遂宁市射洪中学校2022-2023学年高二上学期第一次学月考试数学(理科)试题
解题方法
8 . 如图,在长方体
中,
,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/b5dd2a05-a064-4c45-a2cb-93b7ed2e9ddf.png?resizew=159)
(1)求证:
平面
;
(2)求异面直线
和
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4622aff92fac94916af14f0e913e021.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/13/b5dd2a05-a064-4c45-a2cb-93b7ed2e9ddf.png?resizew=159)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc3f049152c43dd29b12d0a60aa79f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c607775591ff90104cc9c6ce07f919.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83c09eec4e14a861af83d7828797d176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
您最近一年使用:0次
2021-08-24更新
|
769次组卷
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5卷引用:安徽省六安市舒城育才学校2020-2021学年高一下学期5月月考文科数学试题
安徽省六安市舒城育才学校2020-2021学年高一下学期5月月考文科数学试题安徽省六安市舒城育才学校2020-2021学年高一下学期5月月考理科数学试题江西省丰城市第九中学2021-2022学年高一下学期期末检测数学试题(已下线)考点31 直线、平面平行的判定及其性质-备战2022年高考数学一轮复习考点帮(浙江专用)黑龙江省大兴安岭地区呼玛县高级中学2022届高三上学期期末数学(文)试题
9 . 如图,在四棱锥
中,底面
是边长为2的菱形,
底面
,
,
为
的中点,
为
的中点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/bc6774cb-68d0-489a-a610-f248f2dc4ff5.png?resizew=170)
证明:直线
平面
;
求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd47f2c08fb52d822c5c32e0dadd5da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6893fcc2fb37287ccdcbed936f1d3a70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/def4f2e101a80da9bec891ee951b5022.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7719c836a63a80b40efac448d0c6dd2d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/9/bc6774cb-68d0-489a-a610-f248f2dc4ff5.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd19c4db61254be8512edf741bf9f978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3201d3796ed9a29338aac25245a7c8e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
您最近一年使用:0次
2019-07-08更新
|
2441次组卷
|
7卷引用:安徽省郎溪中学2018-2019学高一下学期期末考试数学试题
10 . 如图,在直四棱柱
中,底面
是边长2的正方形,
分别为线段
的中点.
![](https://img.xkw.com/dksih/QBM/2017/8/11/1749750816636928/1749842749145088/STEM/f0215835-9882-4674-8875-a4a50af3c89c.png)
(1)求证:
平面
;
(2)
,求异面直线
与
所成的角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89b866a756d422faec0f7eb229dfaabf.png)
![](https://img.xkw.com/dksih/QBM/2017/8/11/1749750816636928/1749842749145088/STEM/f0215835-9882-4674-8875-a4a50af3c89c.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/679748eab882a6be0fefd2cc300349a4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf90bac174f02c4552e56df4d910bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2017-08-11更新
|
962次组卷
|
3卷引用:安徽省“皖南五十校”2016-2017学年高一下学期末联考数学试题