名校
解题方法
1 . 假设视网膜为一个平面,光在空气中不折射,眼球的成像原理为小孔成像. 思考如下成像原理: 如图,地面内有圆
,其圆心在线段
上,且与线段
交于不与
重合的点
,
地面,且
,
点为人眼所在处,视网膜平面与直线
垂直. 过
点作平面
平行于视网膜平面. 科学家已经证明,这种情况下圆
上任意一点到
点的直线与平面
交点的轨迹(令为曲线
)为椭圆或圆,且由于小孔成像,曲线
与圆
在视网膜平面上的影像是相似的,则当视网膜平面上的圆
的影像为圆时,圆
的半径
为____________ . 当圆
的半径
满足
时,视网膜平面上的圆
的影像的离心率的取值范围为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/137d33c8575602cb3480ba3825dece9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a7442b64b37f685bc3ae88ff450c1a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70e92e4810c9461c39fae1acde95e489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3dc6893e52bbca0d011ac46845334d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
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|
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2卷引用:四川省成都市实验外国语学校2023-2024学年高二上学期期末能力测评数学试题
名校
2 . 已知向量
,若
,则实数
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7612eaf3d84374f6175aa150a1fe93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba87515ee89496c7c9d7c7ff5b9ccdee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5卷引用:广东省中山市华侨中学2023-2024学年高二上学期第二次段考(期中)数学试题
广东省中山市华侨中学2023-2024学年高二上学期第二次段考(期中)数学试题(已下线)模块五 专题2 全真基础模拟2(苏教版高二期中研习)(已下线)高二 模块3 专题1 第2套 小题进阶提升练(苏教版)广东省茂名市高州中学2023-2024学年高一下学期期中考试数学试题(创新班1-3班)(已下线)专题01 空间向量表示及运算--高二期末考点大串讲(苏教版2019选择性必修第二册)
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3 . 已知
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf77c7d1d6c962297fe7d7622ac2f8.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb885a5b92767aa3dd7b3ca28c3488ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf77c7d1d6c962297fe7d7622ac2f8.png)
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解题方法
4 . 若平面
的法向量为
,直线
的方向向量为
,
,则下列四组向量中能使
的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4721537c33310bfe6754dd6a8aa57647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5989bd9142f77fb06cb49b3e5d43d76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1945f382e00ba3feed8c1ea40bb10e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57abcd4537d8a933f85d1f51d716d267.png)
A.![]() ![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
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5 . 已知向量
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e2094728707b54a639e6c51dad8a21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
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5卷引用:福建省南平市2023-2024学年高二上学期期末数学试题
福建省南平市2023-2024学年高二上学期期末数学试题甘肃省天水市第一中学2023-2024学年高二下学期4月学段检测数学试题上海市崇明区2024届高三二模数学试题宁夏回族自治区石嘴山市第三中学2023-2024学年高一下学期5月月考数学试题(已下线)专题03 空间向量及其应用全章复习攻略--高二期末考点大串讲(沪教版2020选修)
名校
解题方法
6 . 设
,
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9745f117d6195d82a7093a8b7ac5726.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d18d5cc420cc3e8a0cc612db4d9b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb6355c7ddd1c545ccf474bb551f095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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解题方法
7 . 已知空间四点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64cd3cac28d66e830fe757f89665b307.png)
A.![]() | B.以![]() ![]() |
C.点O到直线![]() ![]() | D.O,A,B,C四点共面 |
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解题方法
8 . 如图所示,在四棱锥
中,
为等腰直角三角形,且
,四边形ABCD为直角梯形,满足
,
(1)求证
;
(2)若点E为PB的中点,点F为CD的中点,点M为棱AB上一点.当
时,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c025ee3317be1099b7bf03a11e37ed4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa3f47f7c8e18b5e501c9bddeda0a547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/541c76819d18030fa02fcdea0696486f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/15/78fae179-666c-4651-b255-6fa92c4eb091.png?resizew=145)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c71dbf267939080668be464f1aa60da.png)
(2)若点E为PB的中点,点F为CD的中点,点M为棱AB上一点.当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96a2d4b21832458c74b98c2f3428d509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d036bb00a4dbe069c98fa8604559c1dd.png)
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9 . 如图,已知三棱锥
平面
,点
是点
在平面
内的射影,点
在棱
上,且满足
.
(1)求证:
;
(2)求
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2334f72db7d296361167a00790b69031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed00acd878a18a2ac3c932f01ab6200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba2bd1b595743d231779a6818ab02599.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/13/8253122e-7647-4d8c-8e9e-3b72156dc185.png?resizew=126)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3dbf0e4e79a4ed378f9395330a5837b.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6760f565c694d1cdb6d7068e14526d00.png)
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10 . 已知空间中三点
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee3e36b109d9e49eb99cfd16baa0ee05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/922ace9e17f534a1360f8f1c16e7de6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
A.![]() | B.4 | C.3 | D.![]() |
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