1 . 如图,在正方体
中,
,点
为线段
上的一动点,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/df131c7d-ec7a-468b-8b9a-d7ee926a89eb.png?resizew=177)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/14/df131c7d-ec7a-468b-8b9a-d7ee926a89eb.png?resizew=177)
A.![]() |
B.三棱锥![]() |
C.当点P与点![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
2 . 已知正方体
棱长为1,点
是正方体表面上一个动点,满足
,则点
的轨迹长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/4bbba1d8-0432-4e97-9a70-c5e8c00da92c.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ae3720670af14cd8044374a0294be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/16/4bbba1d8-0432-4e97-9a70-c5e8c00da92c.png?resizew=163)
A.2 | B.![]() | C.4 | D.![]() |
您最近一年使用:0次
解题方法
3 . 如图,圆O的半径为2,A是圆内一个定点,且
,B是圆外一个定点,且
,P是圆O上任意一点.线段
的垂直平分线
和半径
相交于点Q,线段
的垂直平分线
和半径OP相交于点R,当点在圆上运动时,点Q和点R的运动轨迹分别是椭圆和双曲线,设它们的离心率分别为
和
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ed6e21185ce4b8eadc7c807806bde5.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f95b221648e1af2e931e72b323290b58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/552c8560b9790cd2349e340b522a3be5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80672dda9430cb42b3136bcb1b67bbad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0101a7b5c8a4aed0de2af363792e39a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13af018556f0b484ed38519f2edc791c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d33558881906c228c262ff8024dcfc4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a33a99190a8fd29c36d5a002e3197cc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ed6e21185ce4b8eadc7c807806bde5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/8662dbb7-f6a9-4abe-9e7b-3dd0a5136130.png?resizew=180)
您最近一年使用:0次
解题方法
4 . 已知直棱柱
中,
,
,
,
,D为线段
上任一点,E,F分别为
,
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/27476bc5-8235-4722-94e4-cb9c91641405.png?resizew=133)
(1)证明:
;
(2)当
为何值时,平面
与平面
的二面角的正弦值最小,并求出最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c14a66ed4bd66df65bc42c4ac1ed15c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41fd676c41d2d644928f014b0fea4689.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f81e24376a13d648c2ed0dc73bc710e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a9c6a736e6eac98a676fa3232db5a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/27476bc5-8235-4722-94e4-cb9c91641405.png?resizew=133)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be099a94f553b5c982d705cc2123e43.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cdc08e1c4a04a18d5ecea03393e36d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27daee2bab56f1808877c2e2594f8324.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
您最近一年使用:0次
解题方法
5 . 已知斜棱柱
中,
,
.设
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/2f22d8ff-5b0c-4715-9280-98af323f674c.png?resizew=136)
(1)用基底
,
,
表示向量
,并求
;
(2)求向量
与向量
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cead0e8eadfdcefa334953e88864f424.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d13ecb54b1006051d2561327aa4755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e984585ddf28c039219afcebf229de7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8780f5b68f8907a57c1c2f96233a78c5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/15/2f22d8ff-5b0c-4715-9280-98af323f674c.png?resizew=136)
(1)用基底
![](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/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2854c67a40773c10bf0a89479d36a0df.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/053c0f6846f2bf8671b351a4263a0270.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af5f1b06a56fc382feed28e01f1ad102.png)
您最近一年使用:0次
6 . 已知点
是直线
上一动点,
与
是圆C:
的两条切线,M、N为切点,则四边形
的最小面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650353eda77d014bb42d185bd967e549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd8b64ef4c3a8c2382adb986d302c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3029ea5516e56e8d20594c71929624f.png)
A.4 | B.![]() | C.2 | D.1 |
您最近一年使用:0次
解题方法
7 . 直线l经过点
,且与直线
垂直,则直线l的一般方程是______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5132a350f40fa8203f9a1a64170f24e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c32c935806559b1a913a7edb3c804999.png)
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解题方法
8 . 已知直线
:
,直线
过点
,且
,则直线
与直线
间的距离是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd9761808026994ab2cd06bc6d5c508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925f7ab39f46f65761e1c88bc222682e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027830fc47290062692964077ee481e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.![]() | B.2 | C.3 | D.![]() |
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解题方法
9 . 已知椭圆T以坐标原点O为对称中心,以坐标轴为对称轴,且过
,
.
(1)求椭圆T的标准方程;
(2)若A、B为椭圆上两点,且以线段AB为直径的圆经过O点.
①求证:
为定值;
②求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f839491380e131c801e2c3c4a75bcdfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f854bbda125255ac766343c1caa71ec.png)
(1)求椭圆T的标准方程;
(2)若A、B为椭圆上两点,且以线段AB为直径的圆经过O点.
①求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/785fc822e5e30c0a9b7fa56d7306809a.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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10 . 已知向量
,
,若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/324a130c5642d10b868d5320a8b0f375.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27f5e7e6301b0718e5cb53a0ba1de6cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf21fef3026cfe445a855c94cab5c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
您最近一年使用:0次