名校
1 . 如图,四边形
是边长为
的正方形,半圆面
平面
,点
为半圆弧
上一动点(点
与点
,
不重合),当直线
与平面
所成角最大时,平面
截四棱锥
外接球的截面面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3e2bed5ce5fe466395d2f5743d335b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f9353ca110c8b81561455b232dbc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/14/48b61d85-2003-4d5d-b3ec-9123fa8e406d.png?resizew=229)
您最近一年使用:0次
名校
解题方法
2 . 如图,在四棱锥
中,底面
为平行四边形,
平面
,点
分别为
的中点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/b6fc5a76-074b-4445-adbe-6e1bfc91c2b4.png?resizew=169)
(1)若
,求直线
与平面
所成角的正弦值;
(2)若直线
与平面
所成角的正弦值的取值范围为
,求平面
与平面
的夹角的余弦值的取值范围.
![](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/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa364dffb98a94fb8285c2cdb9ad14b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9c69a915a625268891ac978dd9a93b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/b6fc5a76-074b-4445-adbe-6e1bfc91c2b4.png?resizew=169)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc532cfe64300cb3da9e04a307c957a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48daee0e42c7dedc3de67e730676edaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
您最近一年使用:0次
2022-11-12更新
|
1196次组卷
|
7卷引用:山西省太原市2022-2023学年高二上学期期中数学试题
3 . 如图,在四棱锥
中,底面
是圆内接四边形,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/3e9b865c-dbd1-4290-bc64-63522775e735.png?resizew=158)
(1)求证:平面
⊥平面
;
(2)若点
在平面
内运动,且
平面
,求直线
与平面
所成角的正弦值的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46a0fbb452d0bea96877053916ae6d92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0bb3b700deb5211897b92b5e5def04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1976b29312c9522c7856ed610c0a0d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/10/3e9b865c-dbd1-4290-bc64-63522775e735.png?resizew=158)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926584088b939200d88e64318f2d4e6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c99cda5a272bbe32b28575fa51b9f6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9a814b70236a108be5d6e7ff271fe92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd17a66a2af938c89e46f22e4d893b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
您最近一年使用:0次
2019-12-07更新
|
893次组卷
|
5卷引用:山西省长治市第二中学2019-2020学年高二上学期期中数学(理)试题
山西省长治市第二中学2019-2020学年高二上学期期中数学(理)试题江苏省徐州市市区部分学校2020-2021学年高三上学期9月学情调研考试数学试题(已下线)专题8.7 利用空间向量求空间角 (精讲)--2021年高考数学(理)一轮复习讲练测(已下线)专题8.7 利用空间向量求空间角(精讲)-2021年高考数学(理)一轮复习学与练(已下线)专题8.7 立体几何中的向量方法(讲)【理】-《2020年高考一轮复习讲练测》
名校
4 . 如图,由直三棱柱
和四棱锥
构成的几何体中,
,平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(I)求证:
;
(II)若M为
中点,求证:
平面
;
(III)在线段BC上(含端点)是否存在点P,使直线DP与平面
所成的角为
?若存在,求
得值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06b3e8bee41beb61f3c4afdc554cb455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba90c0290ae59b9e4f150a48eed8de4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98cf9cb5b6b6de8dd40dce5628d77a1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(I)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a773326771e4d98979061f9949ee0af0.png)
(II)若M为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac480d8d9d7821b62a603cf5cfda236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1477ae90a240deba97f8dadf4d7c41aa.png)
(III)在线段BC上(含端点)是否存在点P,使直线DP与平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1477ae90a240deba97f8dadf4d7c41aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fb46419d4c5868342f6615adcd36d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/5/f028d440-a7d1-4f85-8e59-f48b2e94ba81.png?resizew=148)
您最近一年使用:0次
2018-05-19更新
|
3596次组卷
|
12卷引用:山西省山西大学附属中学2018-2019学年高二上学期期中数学(理)试题
山西省山西大学附属中学2018-2019学年高二上学期期中数学(理)试题2017届北京市海淀区高三下学期期中考试数学理试卷河北省衡水中学2016-2017学年高一下学期期末考试数学(理)试题【全国市级联考】天津市河北区2018年高三二模数学(理)试题湖南省怀化市2018-2019学年高三下学期期末博览联考数学(理)试题(已下线)理科数学-2020年高考押题预测卷01(新课标Ⅰ卷)《2020年高考押题预测卷》2020届天津市第一百中学高考模拟数学试题江苏省苏州市新草桥中学2020-2021学年高三上学期10月月考数学试题湖北省武汉市蔡甸区汉阳一中2020-2021学年高二上学期9月月考数学试题北京市第五十七中学2021-2022学年高二10月月考数学试题北京第五十七中学2020-2021学年高二上学期期末试题北京市东城区第一七一中学2024届高三上学期12月月考数学试题