名校
解题方法
1 . 如图,在四棱锥
中,
,
,E为棱PA的中点,
平面PCD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/a5511bbf-4e03-4355-94ec-8a9be4809877.png?resizew=155)
(1)求AD的长;
(2)若
,平面
平面PBC,求二面角
的大小的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0402dd5ae3db10281f9f1e11738bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/a5511bbf-4e03-4355-94ec-8a9be4809877.png?resizew=155)
(1)求AD的长;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6023d721b0a42f835c94503b5173b068.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1069d514c3c32aeabd274475ee209ed6.png)
您最近一年使用:0次
2021-10-16更新
|
1600次组卷
|
4卷引用:人教B版(2019) 选修第一册 学习帮手 第一章 检测
解题方法
2 . 如图所示,在
中,斜边
,
,将
沿直线AC旋转得到
,设二面角
的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/f175090b-a36a-484f-b450-19cc80ab7896.png?resizew=195)
(1)取AB的中点E,过点E的平面与AC,AD分别交于点F,G,当平面
平面BDC时,求FG的长;
(2)当
时,求二面角
的余弦值.
(3)是否存在
,使得
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd967903ed5a6f640a5b801ec8be0070.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26fdd8e57562ba94e10e7f1d770826d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7ac5396c5ea442e0364b50c1db3d2da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f0ac3005d5ecd6d4cea0ce99a47ef3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05df5a26c2b978503e93efa040b99508.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/f175090b-a36a-484f-b450-19cc80ab7896.png?resizew=195)
(1)取AB的中点E,过点E的平面与AC,AD分别交于点F,G,当平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1fd975b889bfe7ddcec0de56b6f23ee.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33ac762a2899a58faa0d3ab44f1281fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f4b5d1c31f399d19286c4b82abb790.png)
(3)是否存在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d045abc40b9acb8d6d1f4d80cb4655e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
名校
3 . 如图,在四棱锥
中,
平面ABCD,四边形ABCD为正方形,点M,N分别为线段PB,PC上的点,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/63b57030-fd5a-49ba-9fa3-a629f185e43d.png?resizew=346)
(1)求证:当点M不与点P,B重合时,M,N,D,A四点共面.
(2)当
,二面角
的大小为
时,求PN的长.
![](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/8e7784be0caa2ffb58bbebf81fa127c1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/28/63b57030-fd5a-49ba-9fa3-a629f185e43d.png?resizew=346)
(1)求证:当点M不与点P,B重合时,M,N,D,A四点共面.
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f83a04565a8ebaa111894b724b0ba266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f509bdfdc26ae45ee15f5bae8b71823b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
您最近一年使用:0次
2021-10-16更新
|
1353次组卷
|
3卷引用:人教B版(2019) 选修第一册 学习帮手 第一章 1.2.4 二面角
解题方法
4 . 如图,将等腰直角
沿斜边
旋转,使得
到达
的位置,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/b700e49f-33b5-46cf-8904-120b3bf6d21b.png?resizew=157)
(1)证明:平面
平面
.
(2)求二面角
的余弦值.
(3)若在棱
上存在点
,使得
,
,在棱
上存在点
,使得
,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f90f9fba63790e1e5308fa5a1441d71a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/7/b700e49f-33b5-46cf-8904-120b3bf6d21b.png?resizew=157)
(1)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae50ff4c814b581a78346e548964aae7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f1eaa084baa5272450c34ab1ffde54.png)
(3)若在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffb952f86442845da723fd291564484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1a61e889d0b83ed95a38f1adf4e8e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077ad2164c272a0ca4c52f3159b0e486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f5987b311288bb1f71556dfe81d936c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79498e1df1280868532f59ee8059a223.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
5 . 如图,在四棱锥
中,底面
是圆内接四边形.
,
,
.
![](https://img.xkw.com/dksih/QBM/2021/10/1/2820222387773440/2823663732039680/STEM/ec27146f-8080-4912-ab06-3b36590e52ed.png?resizew=262)
(1)求证:平面
平面
;
(2)若点
在
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/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf390ddf4a5fd8106de2a9bd6676a9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac251913cd4ac1f3936e18e4c872d7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1c8e6c6a7c096d0ccb79fa0e2458ce2.png)
![](https://img.xkw.com/dksih/QBM/2021/10/1/2820222387773440/2823663732039680/STEM/ec27146f-8080-4912-ab06-3b36590e52ed.png?resizew=262)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bcbf1197b6a9e629dbd76ba6b8fbd81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357265c532428e886a643e8e653eec9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6ae72f5e5891249caa10c43224da89c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4d41989d897ddb0fe7aa59f3beaabf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1b489c25405ce48699d4f0a62820bed.png)
您最近一年使用:0次
2021-10-06更新
|
1836次组卷
|
7卷引用:重庆市西南大学附属中学2021-2022学年高二上学期第一次定时检测数学试题
重庆市西南大学附属中学2021-2022学年高二上学期第一次定时检测数学试题海南省海口中学2021-2022学年高二上学期期中考试数学试题四川省乐山市十校2021-2022学年高二上学期期中考试数学(理)试题重庆市南开中学校2021-2022学年高二上学期11月月考数学试题(已下线)2022年全国高考乙卷数学(理)试题变式题9-12题(已下线)2022年全国高考乙卷数学(理)试题变式题17-20题(已下线)信息必刷卷02(理科专用)
名校
6 . 如图,在四棱锥
中,平面
平面
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/8fee69d0-04d0-4743-9cfb-dff700246615.png?resizew=183)
(1)求证:
;
(2)求平面
与平面
夹角的余弦值;
(3)若点E在棱
上,且
平面
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6be2b61f4a38e2ee2c1a01e00b3ae6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553d5269397c5cf0909c734464e1b472.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c73eb061b58805586c56ed73f7034fb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6503443cca2402310e480e3be0c47f05.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/8fee69d0-04d0-4743-9cfb-dff700246615.png?resizew=183)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c209827e914ab17f5bc2e6fab044a05.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)若点E在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137fcdac119eff6ac5990b6d201615df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
您最近一年使用:0次
2022-10-21更新
|
1670次组卷
|
12卷引用:辽宁省沈阳市市级重点协作校2021-2022学年上学期高二数学期中联考数学试题
辽宁省沈阳市市级重点协作校2021-2022学年上学期高二数学期中联考数学试题北京市顺义区第一中学2021-2022学年高二上学期期中考试数学试题陕西省渭南市大荔县2021-2022学年高二上学期期末理科数学试题江苏省盐城市2021-2022学年高二下学期期末模拟数学试题重庆市第八中学校2022-2023学年高二上学期期中复习数学试题北京市丰台区2018年高三年级一模数学试题(理)北京市城六区2018届高三一模理科数学解答题分类汇编之立体几何北京市第二十二中学2019-2020学年第一学期期中考试高三数学天津市西青区杨柳青第一中学2022届高三下学期第二次适应性测试数学试题天津市第二中学2022届高三下学期5月线上测试数学试题北京市交通大学附属中学2023届高三上学期12月诊断练习数学试题(已下线)模块十一 立体几何-2
名校
解题方法
7 . 在底面是菱形的四棱锥S-ABCD中,已知
,BS=4,过D作侧面SAB的垂线,垂足O恰为棱BS的中点.
![](https://img.xkw.com/dksih/QBM/2021/4/9/2695932021612544/2809220658454528/STEM/d91a1156-f65a-4102-8aa7-3a482c097645.png?resizew=194)
(1)在棱AD上是否存在一点E,使得OE⊥侧面SBC,若存在求DE的长;若不存在,说明理由.
(2)求二面角B-SC-D的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da05478ac906a1be15a60f629bf08a7.png)
![](https://img.xkw.com/dksih/QBM/2021/4/9/2695932021612544/2809220658454528/STEM/d91a1156-f65a-4102-8aa7-3a482c097645.png?resizew=194)
(1)在棱AD上是否存在一点E,使得OE⊥侧面SBC,若存在求DE的长;若不存在,说明理由.
(2)求二面角B-SC-D的平面角的余弦值.
您最近一年使用:0次
2021-09-16更新
|
1214次组卷
|
2卷引用:浙江省台州市路桥中学2020-2021学年高二下学期返校考数学试题
名校
8 . 如图所示,在四棱锥
中,
平面
,
,
,
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/d32fd212-2871-4a54-a4c1-8675affcb3b8.png?resizew=154)
(1)求证
平面
;
(2)若点
为
的中点,线段
上是否存在一点
,使得平面
平面
?若存在,请确定
的位置;若不存在,请说明理由.
![](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/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10df84d553a8826a7ce9bff4bf0d95b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f78c83425fc00e6e6299a29efce209cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/29/d32fd212-2871-4a54-a4c1-8675affcb3b8.png?resizew=154)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071159cac13097ea0928285bc1be66d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26cf51c6441447f1ba4b15f6c6b20f0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
2021-09-09更新
|
3232次组卷
|
6卷引用:安徽省肥东凯悦中学2021-2022学年高二上学期第三次自主检测数学试题
安徽省肥东凯悦中学2021-2022学年高二上学期第三次自主检测数学试题湖北省恩施州2021-2022学年高三上学期第一次教学质量监测数学试题江苏省南京市金陵中学2021-2022学年高三上学期10月阶段检测数学试题(已下线)专题04 二面角(含探索性问题)-【解题思路培养】2022年高考数学一轮复习解答题拿分秘籍(全国通用版)(已下线)专题35 立体几何中的探索性问题求解策略-学会解题之高三数学万能解题模板【2022版】(已下线)专题36 空间向量在立体几何中的应用-学会解题之高三数学万能解题模板【2022版】
9 . 如图,四边形
是直角梯形,
∥
,
,
,
,
平面
,
为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/db92e7e2-bfd0-43e6-b3af-226dcaeb401d.png?resizew=168)
(1)求证:直线
平面
;
(2)若三棱锥
的体积为
,求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262480ffb55b7617f44b63f130c154a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1134c8e3440abb6cd385af2c169037fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/18/db92e7e2-bfd0-43e6-b3af-226dcaeb401d.png?resizew=168)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c372d059202ec388960b125d4a87dc84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)若三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1601b174c1c0d24b6bc9fbb96c3d701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dac452fbb5ef6dd653e7fbbef639484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f99a8e4053adc8bc59c19bca50ea69.png)
您最近一年使用:0次
10 . 如图,在四棱锥
中,
底面
,四边形
中,
,
.
平面
;
(2)设
,若直线
与平面
所成角大小为30°,求线段
的长.
![](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/c21929cd5ce9120fe3b7ac99730b617b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4aa9084b8fe0fe05c4388d1f835587b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08a9f566f9ab9c6f9498d5c69e9e98bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2021-09-06更新
|
925次组卷
|
3卷引用:上海市西南位育中学2020-2021学年高二下学期期中数学试题
上海市西南位育中学2020-2021学年高二下学期期中数学试题湖北省襄阳市第五中学2021-2022学年高二上学期10月月考数学试题(已下线)广东省佛山市第一中学2024届高三上学期第二次调研数学试题变式题17-22