名校
1 . 如图,在四棱锥
中,平面
平面PAD,
,
,正三角形PAD的边长为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/63ef7254-7a9c-450d-afe9-8204271e4a1c.png?resizew=162)
(1)求证:
平面PAD;
(2)若
,
,求平面PAD与平面PBC所成的锐二面角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413c799e8fb983e6274ec4be9ff6c431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/24/63ef7254-7a9c-450d-afe9-8204271e4a1c.png?resizew=162)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced06b71073e1bb777f326f06016ce17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833cfda415649b832cc136caed392753.png)
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名校
2 . 如图,在三棱柱
中,侧面
为正方形,
;设M是
的中点,满足
,N是BC的中点,P是线段
上的一点.
(1)证明:
平面
;
(2)若
,
,求直线
与平面PMN所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a566b100fb2ebe3d208f9b6527934218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2027fa3dfcde1373ca0222e1358e0c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/12/e6f1d103-14a1-4a6c-8261-f1a5cc952c65.png?resizew=182)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d0edb1508fc95765f3bb316bcb5252d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/105347676853328617bf64545d8546cb.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d768ffd5bf75080e8ff5ce6b472c0cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4f68b8069f0df9e3dbe15c3d7cf5052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b470c4e195cf7a07b7a331ce4b436e03.png)
您最近一年使用:0次
2023-12-12更新
|
361次组卷
|
2卷引用:上海市虹口区2024届高三上学期期终学生学习能力诊断测试数学试题
3 . 如图,三棱锥
中,
,
,
,E为
的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/73000cff-6b06-4c1f-9297-0cc7d5fdc277.png?resizew=186)
(1)证明:
;
(2)点F满足
,求平面
和平面
所成的锐二面角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3d6fb3406ff7fabf9c3b5c7541c67d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9c7cbcc38b28d45c8539710e5b260a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d495d6bb2cf4e141d2055a9f7072018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/27/73000cff-6b06-4c1f-9297-0cc7d5fdc277.png?resizew=186)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0de882caea347e2bd6fcd426caa13b8.png)
(2)点F满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/028a14cd09c33f7e6d9fdc184b5fe64b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ddc76d96d6951ebfef3fe63892a1114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/437bc0b5b7815c77b4956f194fc6ef52.png)
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4 . “直线
垂直于平面
内无数条直线”是“直线
垂直于平面
”的______ 条件.(用“充分非必要”、“必要非充分”、“充要”、“既非充分又非必要”填空)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
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解题方法
5 . 如图所示,在棱长为1的正方体
中,则直线
到平面
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2bf9ef324f1289e205e29fed105c38e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/3/8b2a3939-d251-4a0b-aeaf-8a73dcab11a5.png?resizew=147)
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解题方法
6 . 已知
在异面直线a、b上,且
是异面直线a、b的公垂线段,
,且a与b成30°角,在直线a上取
,则点P到直线b的距离为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602ee324ca5bc3cf9ef251a061b431ab.png)
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2023-10-22更新
|
151次组卷
|
3卷引用:上海市华东师范大学第一附属中学2022-2023学年高二上学期10月月考数学试题
上海市华东师范大学第一附属中学2022-2023学年高二上学期10月月考数学试题上海市大同中学2023-2024学年高二上学期10月月考数学试题(已下线)专题05异面直线间的距离(1个知识点4种题型1种高考考法)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(沪教版2020必修第三册)
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7 . 已知圆锥的顶点为S,底面圆心为O,半径为2,母线SA、SB的长为
,
且M为线段AB的中点.
(1)证明:平面SOM
平面SAB;
(2)求直线SM与平面SOA所成角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ccc37b189fa2cbc269ca0b233dac37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/9/5ce7bf0b-2a87-4c5e-9296-f3302a475e6b.png?resizew=167)
(1)证明:平面SOM
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
(2)求直线SM与平面SOA所成角的大小.
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2023-06-07更新
|
628次组卷
|
2卷引用:上海市华东师范大学第一附属中学2023届高三三模数学试题
名校
8 . 如图,在三棱锥
中,
,O为AC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/36d8828b-c19f-4629-9473-77426f0eaa9e.png?resizew=156)
(1)证明:
⊥平面ABC;
(2)若点M在棱BC上,且二面角
为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e69acb641788897805a6f99236da48a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/25/36d8828b-c19f-4629-9473-77426f0eaa9e.png?resizew=156)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef49a3ca580a144cc65a609c167facc1.png)
(2)若点M在棱BC上,且二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2547225b7d1f17b04a2077258be59ee7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e85ab30d1a7b29a5511f963991affc.png)
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2023-04-23更新
|
2883次组卷
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10卷引用:上海市复兴高级中学2023届高三适应性练习数学试题
上海市复兴高级中学2023届高三适应性练习数学试题浙江省杭州第九中学2021-2022学年高二上学期期末数学试题广东省中山市民众德恒学校2022-2023学年高二上学期第一次段考数学试题河北省石家庄市十八中2022-2023学年高二下学期开学考试数学试题贵州省贵阳市五校2023届高三联合考试(五)理科数学试题福建省2022-2023学年高二上学期11月期中数学试题(已下线)数学(新高考Ⅰ卷)(已下线)数学(上海卷)(已下线)河北省石家庄市2023届高三质量检测(一)数学试题变式题17-22福建省永安市第九中学2023-2024学年高二上学期期中考试数学试题
名校
解题方法
9 . 已知平面
,直线
,
,
,满足
,
,且
,
互为异面直线,则“
且
”是“
”的__ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4042f9c51f83e3367d496e851735d7f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79018590293277ff2d76452a50ad2dbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dedfa42c16dd0aefa2928a6e41f3dba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fed6f6eca4ec7116f707b65bfb4b1d43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e380108ba2cf04e68a5a9393d2b921c.png)
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解题方法
10 . 如图,三棱柱
中,
,若
,则三棱柱
体积最大时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9f23207b67eba6a74de672076c946b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88d52394d0469c11e29bdda390efc71c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a65e51a392df13cf421d4613f24afd19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9f23207b67eba6a74de672076c946b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/4/775be5ee-9c1b-49d2-b78a-49f52ee6f8a6.png?resizew=255)
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