名校
1 . 在四边形
中(如图1),
,将四边形
沿对角线
折成四面体
(如图2所示),使得
,E,F,G分别为
的中点,连接
为平面
内一点,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/67475074-affc-407f-a827-7cd981c3cf8f.png?resizew=325)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f916a90e1e0150e116cef4a3be0d919b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb4c6e9a723aa843e6ba62d7c1a3a6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2a45e3932e7dcd6a02a30d69f42b30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f18ac8d09c5f50a85aff0a730ea51e42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efc8e2514935c60919bb402159abe525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/67475074-affc-407f-a827-7cd981c3cf8f.png?resizew=325)
A.三棱锥![]() ![]() |
B.直线![]() ![]() ![]() |
C.四面体![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2022-08-02更新
|
3220次组卷
|
8卷引用:江苏省南通市如皋市第一中学2021-2022学年高一下学期期末数学试题
江苏省南通市如皋市第一中学2021-2022学年高一下学期期末数学试题江苏省宿迁市沭阳修远中学2021-2022学年高一下学期期末数学试题(已下线)7.3 空间角(精练)(已下线)9.5 空间向量与立体几何江苏省南京师范大学苏州实验学校2022-2023学年高二上学期9月月考数学试题浙江省杭州市源清中学2022-2023学年高二上学期期中数学试题湖北省武昌实验中学2022-2023学年高二上学期10月月考数学试题(已下线)广东实验中学2024届高三上学期第一次阶段考试数学试题变式题11-14
解题方法
2 . 在正方体
中,M是
的中点,点N在该正方体的棱上运动,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
A.当N为棱![]() ![]() |
B.当N为棱![]() ![]() |
C.有且仅有三个点N,使得![]() ![]() |
D.有且仅有四个点N,使得MN与![]() |
您最近一年使用:0次
2022-07-07更新
|
705次组卷
|
4卷引用:江苏省南通市2022-2023学年高一下学期期末模拟数学试题
江苏省南通市2022-2023学年高一下学期期末模拟数学试题广东省佛山市2021-2022学年高一下学期期末数学试题(已下线)突破1.4 空间向量的应用(课时训练)(已下线)模块三 专题3 小题满分挑战练( 2)(苏教版高二)
名校
3 . 由两块直角三角形拼成如图所示的空间立体图形,其中
,当
时,此时
四点外接球的体积为__________ ;异面直线
所成角的余弦为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f8c61f6b83901bcfa65cdc700cb4e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07886ebfa6e27bb00c874bab794e7c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d23be7b8110bb4aed6ca6d54baf0eacf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/19/d40c9fc2-bca7-4c43-9abb-733ff4f49895.png?resizew=151)
您最近一年使用:0次
2021-08-09更新
|
315次组卷
|
4卷引用:江苏省南通市如皋市2020-2021学年高一下学期第二次调研考试数学试题
(已下线)江苏省南通市如皋市2020-2021学年高一下学期第二次调研考试数学试题江苏省南通市2020-2021学年高一下学期期中数学试题江苏省苏州市第十中学2020-2021学年高一下学期5月阶段调研数学试题 (已下线)专题8.7 立体几何中的向量方法(讲)- 2022年高考数学一轮复习讲练测(新教材新高考)
名校
4 . 如图,在四棱锥
中,四边形
是等腰梯形,
.
分别是
的中点,且
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1cbf98ad-109a-4488-bdc9-c09e898e3008.png?resizew=190)
(1)证明:
平面
;
(2)已知三棱锥
的体积为
,求二面角
的大小.
![](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/2e263d46c107fa79a457b642ba035340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7490886e2807c7b8a4fa57d99c4dc3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df7fc746f8c4801d8f2f0471ba3297e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/397dab2cc39244e41e1744214cccb204.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/1cbf98ad-109a-4488-bdc9-c09e898e3008.png?resizew=190)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)已知三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63cd98983166c6f861b82f45bff0e179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c764736ec31656bbd4fe87ca8a593506.png)
您最近一年使用:0次
2021-03-23更新
|
705次组卷
|
5卷引用:江苏省如皋市2020-2021学年高一下学期期中模拟(二)数学试题
名校
解题方法
5 . 如图所示,在直三棱柱
中,
,
,
,
,点
在线段
上.
![](https://img.xkw.com/dksih/QBM/2020/11/20/2597166228307968/2602063705047040/STEM/6de76868667349c1b8a6e54f9ab3814e.png?resizew=235)
(1)若
,求异面直线
和
所成角的余弦值;
(2)若直线
与平面
所成角为
,试确定点
的位置.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae15e5357601ddb7e303b56dbe337145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4b6c682d7b0741fb1f12a073394fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a9394f4b28f399fc860cb6f91ca2a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/2020/11/20/2597166228307968/2602063705047040/STEM/6de76868667349c1b8a6e54f9ab3814e.png?resizew=235)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5dcddf71a68471452cc8c1df24d737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-11-27更新
|
264次组卷
|
8卷引用:2015-2016学年江苏南通中学高一下期中理科数学卷
名校
解题方法
6 . 四棱锥
的底面ABCD是边长为a的菱形,
面ABCD,
,E,F分别是CD,PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/deb77b66-feb9-49c1-921c-38067950f08a.png?resizew=169)
(1)求证:平面
平面PAB;
(2)M是PB上的动点,EM与平面PAB所成的最大角为
,求二面角
的余弦值.
![](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/d07c321ebb740613ff53c1d6e496ee85.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/deb77b66-feb9-49c1-921c-38067950f08a.png?resizew=169)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6501f1c913a4ef64957a2f01ab5baa15.png)
(2)M是PB上的动点,EM与平面PAB所成的最大角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30c20e88a33043f4279fff360c81006e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/242657c0f6a356f2cbdfc23cfff7d3e4.png)
您最近一年使用:0次
2020-08-17更新
|
76次组卷
|
5卷引用:江苏省南通市如皋中学2019-2020学年高一下学期6月第四次阶段考试数学试题
江苏省南通市如皋中学2019-2020学年高一下学期6月第四次阶段考试数学试题河北省石家庄市第二中学2019-2020学年高三下学期0.5模数学(理)试题广东省深圳市宝安中学2020届高三下学期4月模拟数学(理)试题(已下线)专题20 立体几何综合-2020年高考数学(理)母题题源解密(全国Ⅱ专版)(已下线)专题03 立体几何中的动点问题和最值问题-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)
名校
解题方法
7 . 在正方体
中,
为棱
的中点,则异面直线
与
所成角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-08-10更新
|
460次组卷
|
3卷引用:江苏省南通市如皋市2019-2020学年高一下学期期末数学试题
(已下线)江苏省南通市如皋市2019-2020学年高一下学期期末数学试题江苏省南通市如皋中学2020-2021学年高二上学期第二次阶段考试数学试题江苏省南京市第二十九中学2020-2021学年高三上学期学情调研数学试题
名校
解题方法
8 . 在长方体
中,
,E,F为
,
的中点,且三棱锥
的体积为8.
(1)求
的长;
(2)求异面直线BE与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/caa07c3d740f248bf71fd34e4e65a621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28ebd86a076448d19401268f139b5b90.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
(2)求异面直线BE与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f35f348ed8a1690d3ed02aa64459ca50.png)
您最近一年使用:0次
9 . 如图,在长方体
中,底面
是边长为
的正方形,对角线
与
相交于点
,点
为线段
上靠近点
的三等分点,
与底面
所成角为
.
![](https://img.xkw.com/dksih/QBM/2020/7/15/2506642673057792/2507693999398912/STEM/dea9ea77e534478192c2c187e8a9a843.png?resizew=190)
(1)求证:
;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8ea9719021ade22a65c59bd51738763.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://img.xkw.com/dksih/QBM/2020/7/15/2506642673057792/2507693999398912/STEM/dea9ea77e534478192c2c187e8a9a843.png?resizew=190)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/589ddae20626f9aaac616d2a3b5d95bd.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f717b7d4d0978eec7330afec554c078.png)
您最近一年使用:0次
2020-07-17更新
|
139次组卷
|
2卷引用:江苏省南通市如东县2019-2020学年高一下学期期末数学试题
名校
解题方法
10 . 如图,在三棱柱
中,侧面
是菱形,且
,平面
平面
,
,
,O为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/9c8047ef-9991-4d8e-9b1e-b1e0df34c863.png?resizew=251)
(1)求证:
;
(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/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd57614136e2fc269f698a9c3904e31f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9edc50f7febbc2d5d8dcdc23a3630a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37199965a41feed17c44f208b029945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2879880d7d25341a07729b6dd598e4aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/9c8047ef-9991-4d8e-9b1e-b1e0df34c863.png?resizew=251)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74b28e340b30316b567f2f39dd37e1b.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65923116da2971569f512df8b1e8275b.png)
您最近一年使用:0次
2020-05-31更新
|
207次组卷
|
4卷引用:江苏省南通市海门实验学校2019-2020学年高一下学期第三次学情调研数学试题