名校
1 . 如图,四棱锥
中,
平面ABCD,PB与底面所成的角为
,底面ABCD为直角梯形,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c64e3b4f236126ce7f67c9a951d18f2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/11/2cb6a4b2-20cd-4ef8-94dd-dd7955d541a9.png?resizew=220)
(1)求证:平面
平面PCD:
(2)在线段PD上是否存在点E,使CE与平面PAD所成的角为
?若存在,求出有
的值:若不存在,说明理由.
![](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/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c64e3b4f236126ce7f67c9a951d18f2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/11/2cb6a4b2-20cd-4ef8-94dd-dd7955d541a9.png?resizew=220)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
(2)在线段PD上是否存在点E,使CE与平面PAD所成的角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1122194658d429a4c187d6fe4a1c6239.png)
您最近一年使用:0次
2022-07-10更新
|
1805次组卷
|
7卷引用:江苏省苏州市木渎中学、震泽中学2021-2022学年高一下学期期末联考数学试题
江苏省苏州市木渎中学、震泽中学2021-2022学年高一下学期期末联考数学试题福建省福州格致中学2021-2022学年高一下学期期末考试数学试题(已下线)第06讲 向量法求空间角(含探索性问题) (讲)-2江苏省南京市第一中学2022-2023学年高二上学期10月阶段检测数学试题江苏省南京市第一中学2022-2023学年高二下学期期中数学试题(已下线)模块一 专题5 立体几何中的探究问题(已下线)模块一 专题7 立体几何中的探究问题(高一人教B)
解题方法
2 . 如图所示的几何体
中,
平面
,
是
的中点.
![](https://img.xkw.com/dksih/QBM/2022/11/13/3108808518459392/3110391415709696/STEM/b612de94f81343379edf8aa10aedb367.png?resizew=209)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9142a8490de14a87eda628ffa7e28982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd654221ab95fe241d9e0202443f2609.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/788628573da88dd4fd392885661a8ca8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35a0512dbd22d1858bedbf355ab0141.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc56c77464a17a1e97b568762a3e2c6.png)
![](https://img.xkw.com/dksih/QBM/2022/11/13/3108808518459392/3110391415709696/STEM/b612de94f81343379edf8aa10aedb367.png?resizew=209)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3894bd03d1d4b3f8a31df039a5c429d.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55acf08a1fe8bea7a4822d8718dbc09.png)
您最近一年使用:0次
2022-11-15更新
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631次组卷
|
2卷引用:江苏省苏州市2020-2021学年高一下学期期末数学试题
名校
解题方法
3 . 如图,四棱锥
中,
平面
,梯形
满足
,
,且
,
,
为
中点,
,
.
![](https://img.xkw.com/dksih/QBM/2022/4/8/2953847428653056/2954988018180096/STEM/1281fa0d-e31c-4fc4-9d83-71ca57b4c376.png?resizew=192)
(1)求证:
,
,
,
四点共面;
(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/5a1b49f64e0065edad868b25e9fcada3.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/b0fff774b4b0087a6f304ce930d359be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3bbe4cdd2c154bd9a8073b0d4cecb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cafe41f8be1c2f76a83bdcb256a0b61e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc6e4b936d7a800e839a30c3839574d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a41f49f951493ea98541676815dbc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6685ebfea4fe41b318f75e95047e8352.png)
![](https://img.xkw.com/dksih/QBM/2022/4/8/2953847428653056/2954988018180096/STEM/1281fa0d-e31c-4fc4-9d83-71ca57b4c376.png?resizew=192)
(1)求证:
![](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/895dc3dc3a6606ff487a4c4863e18509.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6dd02f171d6ae36135cd30987376e3b7.png)
您最近一年使用:0次
2022-04-10更新
|
1799次组卷
|
5卷引用:江苏省苏州市八校2022-2023学年高一下学期综合质量监测(期末联考)数学试题
名校
解题方法
4 . 如图,已知正方体
的棱长为1,
(t∈[0, 1]),则下列说法正确的有( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/251b5c30-36de-4555-ab3e-4a67e39dc960.png?resizew=167)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/debdc5174cdbcce3354c4e1165ce3749.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/3/251b5c30-36de-4555-ab3e-4a67e39dc960.png?resizew=167)
A.![]() |
B.![]() ![]() |
C.![]() ![]() |
D.若平面![]() ![]() ![]() |
您最近一年使用:0次
2022-01-30更新
|
652次组卷
|
3卷引用:江苏省苏州市2021-2022学年高二上学期期末数学试题
名校
解题方法
5 . 如图,在四棱锥P -ABCD中,底面ABCD是边长为2的菱形,∠DAB=60°,PD⊥底面ABCD,点F为棱PD的中点,二面角
的余弦值为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b8e6f738-4ead-4e15-aecf-bfcfccbb3538.png?resizew=202)
(1)求PD的长;
(2)求异面直线BF与PA所成角的余弦值;
(3)求直线AF与平面BCF所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d733daf111889f16d5404b731d40fd12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f1145c162038df3c7184d9201c628e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/2/b8e6f738-4ead-4e15-aecf-bfcfccbb3538.png?resizew=202)
(1)求PD的长;
(2)求异面直线BF与PA所成角的余弦值;
(3)求直线AF与平面BCF所成角的正弦值.
您最近一年使用:0次
2022-01-30更新
|
720次组卷
|
4卷引用:江苏省苏州市2021-2022学年高二上学期期末数学试题
名校
6 . 已知直三棱柱
中,
,
,
分别为棱
,
的中点,过点
作平面
将此三棱柱分成两部分,其体积分别记为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d57f8dd81c1efd78d01e2cc0a0e8a.png)
__________ ;平面
截此三棱柱的外接球的截面面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b51da47ab8433342f7a319e412fefae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f229274a6e17977cc047814212589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b06ca628c01e7d6711313888921dfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d25115faf05ae128ccac9803d38c5b74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/923d57f8dd81c1efd78d01e2cc0a0e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
2022-01-20更新
|
1130次组卷
|
2卷引用:江苏省苏州市2021-2022学年高三上学期学业质量阳光指标调研数学试题
名校
解题方法
7 . 直三棱柱
中,
,
,点
为线段
的中点,若点
在线段
上,则直线
与平面
所成角的正弦值的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080db3af81b29ed10144a1c2e2a4fb8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fba5d34d3edfc929177ef9af82d5d0bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb88c278e18d776f165bc571031071d8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2021-11-28更新
|
909次组卷
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4卷引用:江苏省苏州市常熟中学2022-2023学年高二上学期一月学业质量校内调研数学试题
江苏省苏州市常熟中学2022-2023学年高二上学期一月学业质量校内调研数学试题福建省泉州第五中学2021-2022学年高二上学期期中检测数学试题(已下线)第06讲 向量法求空间角(含探索性问题) (高频考点—精讲)-1河南省郑州市第一〇二高级中学2023-2024学年高二上学期10月月考数学试题
名校
8 . 已知平面
的一个法向量为
=(2,-2,4),
=(-1,1,-2),则AB所在直线l与平面
的位置关系为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f1a8e551cba7ec9f451749f60e628d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
A.l⊥![]() | B.![]() |
C.l与![]() | D.l∥![]() |
您最近一年使用:0次
2022-01-30更新
|
596次组卷
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18卷引用:江苏省苏州市2021-2022学年高二上学期期末数学试题
江苏省苏州市2021-2022学年高二上学期期末数学试题浙江省金华市十校2017-2018学年高二上学期期末联考数学试题【校级联考】辽宁省实验中学、大连八中、大连二十四中、鞍山一中、东北育才学校2018-2019学年高二上学期期末考试数学(理)试题浙江省舟山市2018-2019学年高二上学期期末数学试题黑龙江省大庆市外国语学校2021-2022学年高二上学期期末考试数学试题【区级联考】山东省青岛市开发区2018-2019学年高二第一学期期中考试数学试题2018年浙江省新高考真训练卷(四)(已下线)考点40 立体几何中的向量方法-证明平行与垂直关系(考点专练)-备战2021年新高考数学一轮复习考点微专题(已下线)1.4.1 空间向量的应用(一)(精讲)-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)(已下线)专题1.2 空间点线面与空间向量(B卷提升篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)苏教版(2019) 选修第二册 限时训练 第7练 空间线面关系的判定浙江省金华市兰溪市第三中学2021-2022学年高二下学期开学考试数学试题江苏省无锡市江阴市第一中学2021-2022学年高二下学期寒假开学测试数学试题广东省江门市台山市华侨中学2022-2023学年高二上学期期中数学试题(已下线)6.3.2空间线面关系的判定(1)4.2 用向量方法研究立体几何中的位置关系 同步练习-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册河北省秦皇岛市青龙满族自治县实验中学2022-2023学年高二下学期开学考试数学试题河北省沧州市河间市第十四中学2023-2024学年高二上学期10月月考数学试题
名校
9 . 如图,在四棱锥
中,侧面
为钝角三角形且垂直于底面
,底面为直角梯形且
,
,
,点
是
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/425340e9-99bb-4b8c-bfbb-2283fb5ec6e3.png?resizew=202)
(1)求证:
平面
;
(2)若直线
与底面
所成的角为
,求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0254c51c4e3e5ca7190cb4cd97defbb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7812ef34a2b02f9ce73952d5db2eee35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a6e2867f32d3f1c3cd36cd3a11a8580.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/425340e9-99bb-4b8c-bfbb-2283fb5ec6e3.png?resizew=202)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ef796b46e68fe77b117ff0483d2370c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/defa5b53043ae802bb1af7d14374406d.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/defa5b53043ae802bb1af7d14374406d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
您最近一年使用:0次
2020-11-30更新
|
1518次组卷
|
6卷引用:江苏省苏州市八校2020-2021学年高三上学期期末联考数学试题
名校
解题方法
10 . 已知正方体
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.![]() ![]() |
B.![]() |
C.线段![]() ![]() ![]() |
D.正方体![]() ![]() ![]() |
您最近一年使用:0次