名校
1 . 已知向量
,
,
.
(1)当
时,若向量
与
垂直,求实数
的值;
(2)若向量
与向量
,
共面,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d5da9382667d04559003325bc360fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e75574d292e3db85d3edfb1be470c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5be8ab25e1c473bf8f729210f0811a.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39d5594493362619a74d98d4aedccd6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/652e029f2a9d029c5f2d2e1407cb26a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d8e782e9687f2e6276a8541ff8dcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45d8e782e9687f2e6276a8541ff8dcf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ff409cd3886c767afb13c9a869c5f23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6570cd7c2f81c9fcffd2c64664f1564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
名校
2 . 如图,在四棱锥
中,底面
是平行四边形,E,F分别为
,
中点.求证:向量
、
、
共面.
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/471ac0f42d01c6d6e094b63628586e4d.png)
您最近一年使用:0次
3 . 如图,四面体
中,
.
(1)求证:平面
平面
;
(2)若
,
①若直线
与平面
所成角为30°,求
的值;
②若
平面
为垂足,直线
与平面
的交点为
.当三棱锥
体积最大时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6c03029467212c952b89696f45456d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/23/2f9a3c3f-41a9-40b4-a456-a8b33158146b.png?resizew=164)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06123e81c41198c76a3335757fac2c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1e156c3e4ffa35ed0ac6526c8d8753d.png)
①若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17622ea6f6f5afd1ad817a557e5889d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d742e749b1140b21512408d555f14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7e4fa04825ac7d071968056322d88be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf4c26f3f4d96117f087400a0f32ece8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be743a99c9d9c2775ced96ccf86d178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f0b8e4d79f6276b0ab054d887183a8.png)
您最近一年使用:0次
2024-04-19更新
|
847次组卷
|
4卷引用:江苏省南京市五所高中学校合作联盟2023-2024学年高二下学期期中学情调研数学试卷
江苏省南京市五所高中学校合作联盟2023-2024学年高二下学期期中学情调研数学试卷(已下线)模块三 专题2 解答题分类练 专题3 空间向量线性运算(苏教版)江苏高二专题02立体几何与空间向量(第二部分)江苏省扬州市扬州中学2023-2024学年高二下学期5月月考数学试题
名校
解题方法
4 . 如图,在直三棱柱
中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba357848ad142aa9148e00fc870bd0ed.png)
分别为
的中点,点Q在线段
上.
时,证明:B,N,M,Q四点共面;
(2)若平面
与平面
夹角的余弦值为
时,求
的长度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/032e8fc105005e7729265e3c323d2f0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e3fdbefa316ae91500cdd733d9b434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba357848ad142aa9148e00fc870bd0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba357848ad142aa9148e00fc870bd0ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427cc63f75859eb6bc743912d0922cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab35850dbc661ded6456b70767cc6cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46da02bc9f46b50f02f4b5eacbe030f8.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c2a027965686aede86ec1843b78962.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e9850904cb6d52d2294b7acbedf418.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a7dd471434c923f76809dfa5ee183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42b618e1cd0f3a7c27816d86fbe3907.png)
您最近一年使用:0次
5 . 已知
,
,
是空间中不共面的向量,若
,
,
.
(1)若
三点共线,求
的值;
(2)若
四点共面,求
的最大值.
![](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/6022390512962b15eb8d1f489976290a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4cff820e10c8532ca92235000718fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20611aba94c5143032630b839569bf80.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28855a0db693584aabac1df99dfade3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
您最近一年使用:0次
名校
6 . 已知空间三点
,
,
.
(1)求以
和
为邻边的平行四边形的面积;
(2)试判别点
与点
,
,
是否共面?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4e53315204d7e67a86c3a7ea33f057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cdb21dcc14a72a18175edc045621cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3323cca16a3da9fed267e0245e515bc8.png)
(1)求以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
(2)试判别点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53d572b6fc1eeb2029b1807e7ffeb963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在长方体
中,
,点E在
上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/b43983df-6e1a-4090-8752-f5aae30706ab.png?resizew=177)
(1)求直线
与
所成角
的余弦值.
(2)在图中画出面
与面
的交线并求出该交线在长方体内部的长度.
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dd33e6492dc76e5e844b3ad6c139a5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1364213f546b37f8764ddcb59e36ae4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/7/b43983df-6e1a-4090-8752-f5aae30706ab.png?resizew=177)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15dc61d5de97b5a40be925b278ae494c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)在图中画出面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f233b375753611ffa7a93c2c12ef5e28.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f233b375753611ffa7a93c2c12ef5e28.png)
您最近一年使用:0次
23-24高二下·江苏·课前预习
8 . 已知三点A,B,C不共线,对平面ABC外一点O,且满足
,判断点P是否与点A,B,C共面.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e8d1585b5b9912f2a69c0f054f5350a.png)
您最近一年使用:0次
2024高二上·江苏·专题练习
9 . 已知
,
,
是三个不共面的向量,
,
,
,且
,
,
,
四点共面,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e73db31aecdde14e0002f082d9091df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2980a18e4d0a2a795b7983a1a1866db7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1821c677712026f8de34fe924b1f52a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b30ac02890469b4716c89e9005e9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a957b6ad6202a90de7da0d61d39f6884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d79639c1de0a711e8747f2535f1395e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
名校
解题方法
10 . 如图,在三棱柱
中,平面
平面
,点
为
的中点,点
在线段
上,且
.
与平面
的夹角的余弦值;
(2)点
在
上,若直线
在平面
内,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df00cdf77ed39ca5a0b305861a693142.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd18ab492e444901bbe9a5a5cb6252a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d35182e303363ec2d2e15e76eb1a4ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99b16cff607cdc2d69afc70dc778acbb.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a7e4a6765ce78b05ee97764771e01f.png)
您最近一年使用:0次
2024-03-04更新
|
821次组卷
|
2卷引用:山东省烟台第一中学2023-2024学年高二下学期2月月考数学试题