1 . 如图,在直三棱柱ABC﹣A1B1C1中,△ABC是边长为6的等边三角形,D,E分别为AA1,BC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/7fe89fd8-1eb9-4e2f-8113-a652182c739c.png?resizew=171)
(1)证明:AE//平面BDC1;
(2)若异面直线BC1与AC所成角的余弦值为
.求DE与平面BDC1所成角的正弦值.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/26/7fe89fd8-1eb9-4e2f-8113-a652182c739c.png?resizew=171)
(1)证明:AE//平面BDC1;
(2)若异面直线BC1与AC所成角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
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19-20高二·浙江·期末
名校
2 . 如图所示四棱锥
中,
底面
,四边形
中,
,
,
,
,
为
的中点,
为
中点.
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412911289155584/2412954668687360/STEM/a3dbb57fb4c84ffa84bec7b9146a0a4c.png?resizew=223)
(1)求证:
平面
;
(2)求直线
与平面
所成的角的正弦值.
![](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/d5acb763021bf166ca719d07223591d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81981fd7b343f4fe2db8f36eb66c1ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/2020/3/5/2412911289155584/2412954668687360/STEM/a3dbb57fb4c84ffa84bec7b9146a0a4c.png?resizew=223)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c8ccd4181f956f6e0140bf0ab8f0716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
您最近一年使用:0次
2020-03-05更新
|
476次组卷
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4卷引用:福建省南安市侨光中学2020-2021学年高二上学期第一次阶段考试数学试题
名校
解题方法
3 . 如图,在几何体
中,四边形
为菱形,且
,
平面
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/d92d609b-6d32-4e50-9364-38b91fed2b41.png?resizew=239)
(1)求证:平面
平面
;
(2)
为
中点,当
,
时,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a22d6b860f06fe23618b0d3de6768fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2622edcd2b9e514734ded7fbec3f7c6c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/15/d92d609b-6d32-4e50-9364-38b91fed2b41.png?resizew=239)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8dc6db50a9709c3f4d84eee7bdf1250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a19338598965bb3856cdd0236bbf694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803e96e7ccd7a84c1d87c394f271223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdfe0538ece1daca775b1c0d3fad69d4.png)
您最近一年使用:0次
2020-03-22更新
|
316次组卷
|
3卷引用:2020届福建省福州第一中学高三下学期教学反馈检测数学(理)试题
解题方法
4 . 如图,三棱柱
的底面是正三角形,
底面
,M为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/fd25ad21-150c-48aa-97cb-88d5506c9c73.png?resizew=182)
(1)求证:
平面
;
(2)若
,且沿侧棱
展开三棱柱的侧面,得到的侧面展开图的对角线长为
,求作点
在平面
内的射影H,请说明作法和理由,并求线段AH的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5845ccc0d735dc14c92a8926d9b1def6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/fd25ad21-150c-48aa-97cb-88d5506c9c73.png?resizew=182)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/547a4b438e2e6687c7cd55ea08bbaae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc416a5b8dc234628e7475387888d82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dafaeda9177baa0f937f58f680de448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46b91c857bbe3c4f0f08dd2a4124a96e.png)
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名校
5 . 已知函数
.
(1)讨论
的单调区间;
(2)当
且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5982b422c4168ec4b7e238e52b276d.png)
(1)讨论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c7b69e93488fcd2a195cb9793e94fc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99b13836d1afbbec124efb3fbfd7582.png)
您最近一年使用:0次
名校
6 . 如图,已知⊙O的直径AB=3,点C为⊙O上异于A,B的一点,
平面ABC,且
,点M为线段VB的中点.
![](https://img.xkw.com/dksih/QBM/2020/2/21/2404029505863680/2404684088008704/STEM/19dae500-57a0-469c-9e1f-f3be64c066ad.png)
(1)求证:
平面VAC;
(2)若AB与平面VAC所成角的余弦值为
,求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d01592b7e10bf087d1465f9d6899bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df494545dda7eefbcd863cd8b3c9a81.png)
![](https://img.xkw.com/dksih/QBM/2020/2/21/2404029505863680/2404684088008704/STEM/19dae500-57a0-469c-9e1f-f3be64c066ad.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
(2)若AB与平面VAC所成角的余弦值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a99e85631aa0ebd7cbee3ac5a20aa727.png)
您最近一年使用:0次
2020-02-22更新
|
554次组卷
|
2卷引用:福建省厦门双十中学2018-2019学年高二下学期第二次月考数学(理)试题
名校
7 . 如图,平行四边形ABCD中,E,F分别是AD,AB的中点,G为BE与DF的交点.若
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/d6c07df7-3117-4f63-8487-ad6539a63675.png?resizew=168)
(1)试以
,
为基底表示
,
;
(2)求证:A,G,C三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1887a1513aee097a396e99d7399c4e22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3afb528b6095c9db39b8aa899a33427.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/1/d6c07df7-3117-4f63-8487-ad6539a63675.png?resizew=168)
(1)试以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6cbb6f308715ba2e58c11e61dc7d61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d6d630148aa58959960d8568a66742a.png)
(2)求证:A,G,C三点共线.
您最近一年使用:0次
2020-02-05更新
|
1933次组卷
|
9卷引用:福建省泉州市鲤城北大培文学校2020-2021学年高一下学期期中考试数学试题
福建省泉州市鲤城北大培文学校2020-2021学年高一下学期期中考试数学试题辽宁省锦州市2019-2020学年高一上学期期末数学试题(已下线)【新东方】双师212高一下辽宁省辽河油田第二高级中学2020-2021学年高一3月开学考试数学试题(已下线)第9章 平面向量(提高卷)-2020-2021学年高一数学十分钟同步课堂专练(苏教版2019必修第二册)(已下线)专题9.3 向量基本定理及坐标表示(基础练)-2020-2021学年高一数学十分钟同步课堂专练(苏教版2019必修第二册)广西梧州市岑溪市2021-2022学年高一下学期期中考试数学试题云南省保山市腾冲市第八中学2022-2023学年高一下学期期中考试数学试卷江苏省常州市第二中学2023-2024学年高一下学期3月月考数学试卷
解题方法
8 . 已知函数
(
),
.
(1)当
时,
与
在定义域上的单调性相反,求b的取值范围;
(2)设
,
是函数
的两个零点,且
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34449685b69dfe18b065566ea0367149.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73254f32b6da29ecc32df2e9f87a4c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3fe13941d942ae8917af15707ceeca3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f22a4a0dd7307a1323d25331e60782d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d8dafc71b106f39f4e15442220897b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efd845d5b7989956bce410362fb4f974.png)
您最近一年使用:0次
9 . 如图,四棱锥
中,
平面ABCD,
,
,
,
,E为PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/4d5e559a-0e32-474e-828d-804efdf936db.png?resizew=200)
(1)求证:
平面PDC;
(2)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/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68d31600cba2d5256c7e78b6122d6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc659b6ee1e3eeaa00e3329d5626057d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/4d5e559a-0e32-474e-828d-804efdf936db.png?resizew=200)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a242bac17529360ce88767f7270facd3.png)
您最近一年使用:0次
10 . 如图,在三棱锥
中,
为正三角形,
为棱
的中点,
,
,平面
平面
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/1b56568e-cd28-4065-a671-4ca3b7e6e511.png?resizew=141)
(1)求证:
平面
;
(2)若
,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63ab13ef156d034b710d811e09b0be34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36c4559d27e3905980d1a4f1856f07de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5002471e69d992c4d10c8255ba152e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/1b56568e-cd28-4065-a671-4ca3b7e6e511.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0628681907ac8d7fdb94d8bc1b15feb9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bb5b12692517a39c320f99a479eb055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e351795b12a190463b86d3cd9c84a823.png)
您最近一年使用:0次
2019-11-05更新
|
1493次组卷
|
6卷引用:2020届福建省仙游县枫亭中学高三上学期期中数学(文)试题