名校
解题方法
1 . 如图,四棱锥
中,
平面
,底面是边长为2的菱形,
,点E、F、G分别为线段CD、PD、PB的中点.
平面PAD;
(2)求平面AFG与平面PBC夹角的余弦值;
(3)设直线PC与平面AFG的交点为Q,求四边形AFQG的面积.
![](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/764dcbb8b7857a698a7333175184e098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f31d54d125c042169e282f14eddd45a1.png)
(2)求平面AFG与平面PBC夹角的余弦值;
(3)设直线PC与平面AFG的交点为Q,求四边形AFQG的面积.
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名校
解题方法
2 . 已知空间三点
,
,
,
.
(1)求以
,
为邻边的平行四边形的面积;
(2)若D点在平面
上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc332e0792bd16486a61c1658ccfecf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00932ea296bbcfc79a61e53e4d64b7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb309e7396189da4645425f2ea697055.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f21a7ba16850aa3aff47d53ab5a7d45.png)
(1)求以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若D点在平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
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3 . 已知向量
.
(1)求
;
(2)若向量
与向量
共面,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8feb8d57eb5b58f06419b8a71c67894.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/596a3ee5d8473fc6619ea7730e13325b.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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名校
4 . 如图,在四棱锥
中,
平面
,
,
,
,
.
为
的中点,点
在
上,且
,点
在
上,且
.
(1)求证:
平面
;
(2)求平面
与平面
的夹角的余弦值.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a923784f083b7f4777891afe06b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.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://staticzujuan.xkw.com/quesimg/Upload/formula/f88454ace46996b99361d18e76189cdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/557010ef2b20618df4771ac66daef18f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/27/08493c7f-1e08-4a5c-bd9b-099556aeaa1a.png?resizew=172)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331da51a299acaaafa61551d0ebd3e79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e106f4233be16e98f2c1bf9f1635622.png)
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2023-06-22更新
|
370次组卷
|
4卷引用:福建省莆田第一中学2022-2023学年高二下学期6月月考数学试题
福建省莆田第一中学2022-2023学年高二下学期6月月考数学试题江西省全南中学2022-2023学年高二下学期期末教学质量验收数学试题(已下线)模块三 专题4 空间向量的应用1直线与平面的夹角、二面角 B能力卷(已下线)模块三 专题5 直线与平面的夹角、二面角 B能力卷 (人教B)
名校
解题方法
5 . 如图所示,直角梯形
和三角形
所在平面互相垂直,
,
,
,
,异面直线DE与AC所成角为
,点F,G分别为CE,BC的中点,点H是线段
靠近点G的三等分点.
四点共面;
(2)求二面角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad3a079cfdcca9acdacecbf08f9f78cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e223e3b657fe3f5856303f80a276fa0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60fe9421954bd2a0d39cf229d32ef19c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1c4c2f7b1b8987384e5c9ea1075750d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10134e7a46e6f6f7cb9d5e2371727d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b0f98b5f267c1981470e883828c94d6.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25cdb80b7b845972f362d9eba8cb95f5.png)
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2023-05-20更新
|
540次组卷
|
4卷引用:福建省厦门外国语学校2023-2024学年高二上学期10月阶段性检测数学试题
名校
解题方法
6 . 如图所示,在平行六面体
中,E、F分别在
和
上,且
,
.
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074849500233728/3075541171716096/STEM/a7115b76f21a4de68ed810c2f901420f.png?resizew=206)
(1)证明
四点共面;
(2)若
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1859959fdb4c5edd8056893f94a10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c0b233487d441fe21ec26266eb0c6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1608899e256364c9c9c3cb47ac420d12.png)
![](https://img.xkw.com/dksih/QBM/2022/9/26/3074849500233728/3075541171716096/STEM/a7115b76f21a4de68ed810c2f901420f.png?resizew=206)
(1)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821f1b9f4bb03e0d9e5db8e0b4683070.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6c7bcd0581b645e345febce51cf5f53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1433c8103033c67232f2f9ae189608d.png)
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2022-09-27更新
|
732次组卷
|
6卷引用:福建省平山中学、内坑中学、磁灶中学、永春二中、永和中学2023-2024学年高二上学期期中联考数学试题
福建省平山中学、内坑中学、磁灶中学、永春二中、永和中学2023-2024学年高二上学期期中联考数学试题山东省济宁市汶上县第一中学2022-2023学年高二上学期第一次模块检测数学试题山东省东营市广饶县第一中学2022-2023学年高二上学期10月月考数学试题(已下线)模块一 专题1 空间向量的基本运算 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)模块一 专题1 空间向量的基本运算 期末终极研习室(2023-2024学年第一学期)高二人教A版(已下线)6.1 空间向量及其运算(4)
7 . 如图,在边长为3的正方体
中,点P,Q,R分别在AB,
,
上,且AP=
=1,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3db1494a1d927f971490c18a54cbcce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/17e95837-2109-42e4-9ca2-227096bfdce4.png?resizew=197)
(1)求点D到平面PQR的距离
(2)判断点N是否在平面PQR内,并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e3334853138fb74687d66b1e45f2fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d105ed140e47249d237dbdfda67ef131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3db1494a1d927f971490c18a54cbcce.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/28/17e95837-2109-42e4-9ca2-227096bfdce4.png?resizew=197)
(1)求点D到平面PQR的距离
(2)判断点N是否在平面PQR内,并证明你的结论.
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2022-01-09更新
|
248次组卷
|
2卷引用:福建省泉州市2021-2022学年高二上学期期中联考数学试题
8 . 已知E,F,G,H分别是空间四边形ABCD的边AB,BC,CD,DA的中点.
![](https://img.xkw.com/dksih/QBM/2021/12/30/2883785260703744/2885873556455424/STEM/1c8f5b2d-aaa7-494e-86b5-cbcfa9ab717e.png?resizew=234)
(1)用向量法证明E,F,G,H四点共面;
(2)设M是EG和FH的交点,求证:对空间任一点O,有
.
![](https://img.xkw.com/dksih/QBM/2021/12/30/2883785260703744/2885873556455424/STEM/1c8f5b2d-aaa7-494e-86b5-cbcfa9ab717e.png?resizew=234)
(1)用向量法证明E,F,G,H四点共面;
(2)设M是EG和FH的交点,求证:对空间任一点O,有
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1696ba7e9fc3f3b9837032c87f7fc8.png)
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名校
9 . 已知空间中三点
,
,
,设
,
.
(1)若
,且
,求向量
;
(2)已知向量
与
互相垂直,求
的值;
(3)若点
在平面
上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b5e428213f946350934bc876fba5514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daca2df16b221585c93109fd17bc1b5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b92ecb2412db3b9143c500555c2a0ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bad658e33513bf106d1d6bda984d07f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194aa0f2aebeb41be06303f4977a7155.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd78df4d1bb3faf885b0dbfdffa6dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42e495553df9044a952d54bdde82416.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
(2)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41960bbc66bdc3b28be0138f83f9de5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f504623fad7409aa53c842ec25461da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2021-10-03更新
|
975次组卷
|
8卷引用:福建省厦门大学附属科技中学2022-2023学年高二上学期10月月考数学试题
福建省厦门大学附属科技中学2022-2023学年高二上学期10月月考数学试题北京市育英学校2020-2021学年高二上学期期末考试数学试题云南省永善县第一中学2021-2022学年高一9月月考数学试题广东省深圳市厚德书院2021-2022学年高二上学期10月月考数学试题广东省广州市第六十五中学2022-2023学年高二上学期10月月考数学试题(已下线)高二上学期期末【全真模拟卷02】-2022-2023学年高二数学考试满分全攻略(人教A版2019选修)广东省广州市第一一三中学2023-2024学年高二上学期10月月考数学试题云南省玉溪市新平县第一中学2021-2022学年高二上学期期末素质测试数学试题