名校
1 . 在正方体
中,
分别为棱
,
,
的中点,则下列直线与
垂直的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b199a99e53d67ff4abf233930961a29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e391dbcb3ecb829c1f6c986b2181e3d4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2 . 若直线
,且
的一个方向向量为
,平面
的一个法向量为
,则
为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff259ba50b735db32427fc0ebfbdfdaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4afce3be62b4ac30f198f3b845ef70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b855b4ec50f335abcb59317a0727d2e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 已知空间四边形
中,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3241d7fedd89d85711acd7a2635298af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b5f7fd37cdb01d649bd074bc79d7339.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9acdabbbcfa6185a39659a416a4218.png)
您最近一年使用:0次
解题方法
4 . (1)设两条异面直线
的方向向量分别为
,求直线
与直线
所成的角的大小.
(2)设直线
的方向向量为
,平面
的法向量为
,求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632244ea6931507f8656e1cc3437d392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac182876689b6fb152584d36c457e527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/943b14c3138e9b0929b34ad6c48459f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb90e56c0f605ad6d6c97de4203b3dce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
您最近一年使用:0次
5 . 设
是空间向量的一个单位正交基底,则向量
,
的坐标分别是______ ;______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/808173f5aafa97a38056d68247d68314.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a96673e9266606fbb163f682b5f99326.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6b1ae5eb55c8f6665e8a37741b504d.png)
您最近一年使用:0次
6 . 下列说法正确的是( )
A.已知点![]() ![]() ![]() ![]() ![]() |
B.已知点![]() ![]() ![]() ![]() ![]() |
C.已知点![]() ![]() ![]() ![]() ![]() |
D.已知点![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
名校
7 . 已知直线l的方向向量为
,平面
的法向量为
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1836384aa59e97841686b3dd6f255a5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02e49798cc33aca11cab97d47db10ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e380108ba2cf04e68a5a9393d2b921c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/934d37c81b2266c7b86bcc11afaf5f91.png)
A.2 | B.3 |
C.4 | D.5 |
您最近一年使用:0次
名校
8 . 如图,正三棱柱
的侧棱长为4,底面边长为2,D为
的中点.
(1)以
为空间的一组基底表示向量
,
.
(2)线段
上是否存在一点E,使得
?若存在,求
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/98d61d4a-7ee2-427c-86a9-7a890e1a9cc8.png?resizew=140)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b104831ce8f0486de0faf40d5b24d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4781e3daa2c4e018ca0ae09bb56abc0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e3bb3bbf00f936aa72c9d39e5a0879.png)
(2)线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fd4c85bb98a2a0afddd7ed92578ad2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84be64d28b1623e71ad989f37336b1f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee8a62b00067eaad13a3204ad6e4b1c8.png)
您最近一年使用:0次
名校
解题方法
9 . 在所有棱长都为2的正四棱锥
中,侧棱
与侧面
和底面
所成的角分别为
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14462b51a239b9047a545f5a3e6f9333.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14462b51a239b9047a545f5a3e6f9333.png)
您最近一年使用:0次
10 . 如图,在正四棱柱
中,
,
,E为棱
上的一个动点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55a2310cbba5e050488cd9296eb195d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/556be936-1b54-4018-9aab-92bb43564976.png?resizew=137)
A.![]() | B.三棱锥![]() |
C.存在点E,使得![]() ![]() | D.存在点E,使得![]() ![]() |
您最近一年使用:0次
2023-11-07更新
|
461次组卷
|
4卷引用:吉林省松原市前郭尔罗斯蒙古族自治县第五高级中学2023-2024学年高二上学期期中数学试题