解题方法
1 . 在矩形
中,
,
,沿对角线
将矩形折成一个大小为
的二面角
,当点B与点D之间的距离为3时![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4961a7dd688b8a12db7d1d3480c6b87f.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4746df85049d1651d3f6c30212a7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c909cd1b6f3fa1ec39eb245e8f5c11c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4961a7dd688b8a12db7d1d3480c6b87f.png)
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2 . 如图,四棱柱
的底面
是正方形,
,
且
,则
( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/9/f0b6c12c-5004-4501-9ac6-8d8e0d541b09.png?resizew=169)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ce64c7cf095a20894e9ddd0d95992a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63bc887cc71a3a91c1b2070d953b82b4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/9/f0b6c12c-5004-4501-9ac6-8d8e0d541b09.png?resizew=169)
A.4 | B.0 | C.![]() | D.![]() |
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名校
3 . 三阶行列式是解决复杂代数运算的算法,其运算法则如下:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c971b2ecdfce17d75d0290dd194baa3b.png)
.若
,则称
为空间向量
与
的叉乘,其中
,
,
为单位正交基底.以
为坐标原点,分别以
的方向为
轴、
轴、
轴的正方向建立空间直角坐标系,已知
是空间直角坐标系中异于
的不同两点.
(1)①若
,求
;
②证明:
.
(2)记
的面积为
,证明:
;
(3)问:
的几何意义表示以
为底面、
为高的三棱锥体积的多少倍?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c971b2ecdfce17d75d0290dd194baa3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b759f4d0af0d28b35bdd5648db70968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b44b6a86302386ebf96b784d02b039c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4e6bae1b67a0a1eeafdd1114a792df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0f4837cd4b882c0380201dd437e7ae1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2772831f709c3c7c9a334b9444e0504.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808173f5aafa97a38056d68247d68314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4664eed9e1abab0ed6397c58d70e731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faea453a5148e6b281c75a0caa793452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00db2bada2cfc90c5213aca8af17df4c.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f36900d061dee46d3f76344ac576ba1.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29aa828f2bd9a5e63ee58dcaa9d0d336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd55f2f03192e5f0d76bf1cdb51872f2.png)
(3)问:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db0cfd110195cf5e453947d1648ef605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4124e7ab7a93ee45858b3a4d4ab3508b.png)
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3卷引用:压轴题04立体几何压轴题10题型汇总-2
4 . 如图,在四面体
中,
分别是
上的点,且
是
和
的交点,以
为基底表示
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42c2d86d8daea5e652d99fe1c6bc3f9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a337a934b801730321f67b0e5a0b144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b85a08b7404da7ee0fa373540966176b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e55e398e8520d8a36fb5a625a085b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83f1f880e5ffbff036953acaca90c41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1408c55c40465b26758562f59d99ae41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe6d728b430549f00bb9c0a7bf8bf7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ce0da153621bbd05519f168b527e3e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/28/fb89f17c-87a6-403f-bc75-f41656266583.png?resizew=154)
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5 . 在正方体
中,点
满足
,其中
,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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35f1889b7700cfc41b1b6f75909eb35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2a6234f8d5cb65e04b58cd19650885.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若点![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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6 . 在四面体
中,M点在线段
上,且
,G是
的重心,已知
,
,
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebe72d1b634f1e89d8699e605e7d46af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420ad6159fc091d6a5ffddf0676d2662.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68c2e7e9fd8519fd1c293cc577408263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a40f8ef7e3af00c41f85a20578afdb57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da53a4722fb7b67eeb4145b491c456ff.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-02-28更新
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231次组卷
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3卷引用:第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点4 空间向量基底法(四)【基础版】
(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点4 空间向量基底法(四)【基础版】湖北省荆门市2023-2024学年高二上学期1月期末学业水平检测数学试题江苏省常州市联盟学校2023-2024学年高二下学期3月阶段调研数学试题
7 . 如图,在平行六面体
中,
,
,
,
,则
等于( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/25d9bca4-001c-4792-978a-66ade22a8463.png?resizew=138)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57c6b0a6cb307c4c02f503831862f7d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ecbca919bff5a39a99dd7f867dd61f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f13a7e088e027e8e0120810deae72d6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/19/25d9bca4-001c-4792-978a-66ade22a8463.png?resizew=138)
A.![]() | B.![]() | C.![]() | D.10 |
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2024-02-06更新
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3卷引用:第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点5 空间向量基底法综合训练【基础版】
(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点5 空间向量基底法综合训练【基础版】河南省信阳市固始县2023-2024学年高二上学期期末考试数学试卷河南省信阳市2023-2024学年高二上学期期末教学质量检测数学试题
8 . 已知空间向量
的模长分别为1,2,3,且两两夹角均为
,点
为
的重心,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ad85b1b027a45ce5cbde9ed1fd9632.png)
_____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12e912c56b58fc780489fab055aa94b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ad85b1b027a45ce5cbde9ed1fd9632.png)
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9 . 如图,在四棱锥
中,底面
为菱形,
,
为棱
的中点,且
,则
( )
![](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/bb0801140c44af357abde040b5299d74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a155eabb40d28785adc2d53fcce779e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d476da94dcade5f83541f3fca22a1039.png)
A.6 | B.8 | C.9 | D.10 |
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6卷引用:第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点4 空间向量基底法(四)【基础版】
(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点4 空间向量基底法(四)【基础版】河南省部分名校2023-2024学年高二上学期1月期末考试数学试题河南省焦作市2023-2024学年高二上学期1月期末考试数学试题河南省濮阳市2023-2024学年高二上学期期末考试数学试题河南省周口市沈丘县第三高级中学2023-2024学年高二上学期期末数学试题山东省东营市第一中学2023-2024学年高二下学期开学收心考试数学试题
10 . 如图,四面体
的所有棱长均为2,D,F分别为
,
的中点,且点E为
的三等分点(靠近点B).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/1e969929-e6e1-422d-8245-f4856eea71f3.png?resizew=160)
(1)设向量
,
,
,用
,
,
表示向量
;
(2)求点D到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334a5773c8d24f29ec3231075170e4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c77e9c89b7275b0c1a9af5c9a72e5968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/11/1e969929-e6e1-422d-8245-f4856eea71f3.png?resizew=160)
(1)设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fbd0a772a009eec08ec6d50a59eae67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7824b7ecd7d62f8a76a05c88bfd6693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95e02cdf7ad2557cd1e92a8b438a9f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa8c53645db602c72b00b599c2c0ff97.png)
(2)求点D到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3747e528a1e8d45668ccf835c0175a73.png)
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2024-01-22更新
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140次组卷
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4卷引用:第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点3 空间向量基底法(三)【基础版】
(已下线)第七章 应用空间向量解立体几何问题拓展 专题一 空间向量基底法 微点3 空间向量基底法(三)【基础版】四川省巴中市2023-2024学年高二上学期期末考试数学试卷四川省遂宁市2023-2024学年高二上学期期末质量监测数学试题四川省雅安市2023-2024学年高二上学期期末教学质量检测数学试题