1 . 如图,在四棱锥
中,底面ABCD是边长为2的菱形,
,
是等边三角形,平面
平面
,M为PC的中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/4f7336c0-62aa-428c-952f-f69ac3bc9831.png?resizew=186)
(1)求证:
平面
;
(2)求MD与平面ABCD所成角的正弦值;
(3)设点N在线段PB上,且
,PA的中点为Q,判断点Q与平面MND的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df793f5dac174bc71bd1e82bbf5732b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55a675310c8ba418e5a59beb7317e21e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93edc7bb513f40a89173121c8570cd65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/4f7336c0-62aa-428c-952f-f69ac3bc9831.png?resizew=186)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/373f735f0f04d11f1951eaef1bb78b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9af29254fe60a392c249c5791279e9c8.png)
(2)求MD与平面ABCD所成角的正弦值;
(3)设点N在线段PB上,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc7d2ae54c0fdc68c979b6ca6cd9652.png)
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名校
2 . 已知平面
的法向量为
,
,若直线AB与平面
平行.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46ed3259d3513d161c27bd01039a0750.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc4fbeeef1fc01d22ffe929411ceea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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3 . 已知空间向量
,
,
.
(1)若
与
互相垂直,求实数
的值;
(2)若
,且
与
互相平行,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419830a9851022b7da1b6dc632d90e70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9162f6b251803ff1c49fa8e878d0ad1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/575e86e6694ee62509c73481f46b8204.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a06c8eae3652486cf9e416ce3a8ffc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496eeab5938122aa57a7fc521ef7c469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40436543cc51f42b5b5d93e55a407ce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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4 . 已知向量
,
,
.
(1)若
,求实数
的值;
(2)求
;
(3)若
,
,
不能构成空间向量的一个基底,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74eaff36755a7fc339de501c69365c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cb48bdda5932311abf16f32339c4c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7a28090124c5ed4e4762f5dde65c404.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1c5bcaa260128e281a12f6ef6aacbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3db87f99222f1705e122a6bd329c9f1.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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5 . 已知空间三点
,
,
,在直线
上有一点
满足
,则点
的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4098582bf9572f219d7a7d1f30562d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dba8b97ce3df77b96144375b93c9ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85ec3e4471201712b376ac2df7d699f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3440101c3caaf8e7f75d06d9e2a56b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
6 . 如图,在棱长为4的正方体
中,点P是线段AC上的动点(包含端点),点E在线段
上,且
,给出下列四个结论:
平面
;
②存在点P,使得
是等腰直角三角形;
③若
,则点P轨迹的长度为
;
④当
时,则平面
截正方体
所得截面图形的面积为18.
其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88243f7cd807f10443edc21afcb5c5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc94668eedf6e35712b0e56098840694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73845d4d663b3de0b281611fe2c762fe.png)
②存在点P,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0058da71a42b3992b8f25ad1a5089b5.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055cc63a832e9ff2f4697d876ee1d78b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b76f4be8e9f87f3b21e32b6c7c5cfc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17479979d3e99a50ff4ee2491580f11e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
其中所有正确结论的序号是
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7 . 已知向量
,
,且
,则实数
的值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/488048c1f972a0a70355fb8fabeea4a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e1a5867c9a061c1cf03e30ae8e9c3a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.4 | B.![]() | C.2 | D.![]() |
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北京市顺义区第一中学2023-2024学年高二上学期期中考试数学试题北京市中国人民大学附属中学2022-2023学年高二上学期数学期末复习试题(2)山东省临沂市莒南第一中学2022-2023学年高二上学期期末数学试题(已下线)高二数学上学期期末模拟试卷01(选择性必修第一册+数列)-【题型分类归纳】2022-2023学年高二数学同步讲与练(人教A版2019选择性必修第二册)重庆市杨家坪中学2022-2023学年高二上学期期末数学试题
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8 . 若直线l的方向向量为
,平面α的法向量为
,且
,则m的值( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ee53f22c1fbdcf77214547c4d8e04e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0366d1bb8f87037e59b60e2ea2022e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82466bf84ee856b132578d0e6d3e82b5.png)
A.![]() | B.![]() | C.4 | D.![]() |
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9 . 已知空间向量
,则“
”是“
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f43d9791895f186feb8ee47fccc404c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5aa846a5b7c96fe2ce665eb1ea5f0e.png)
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
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10 . 已知
=(2,3,1),
=(-4,2,x)且
⊥
,则|
|=______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23bd18136e4e71e1e267bc9f8634b932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec82bd4e0fb7887e5999b8220f60b073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23bd18136e4e71e1e267bc9f8634b932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec82bd4e0fb7887e5999b8220f60b073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec82bd4e0fb7887e5999b8220f60b073.png)
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