真题
解题方法
1 . 设向量
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de90ebc599dee1d3dec0733f0ddf83bc.png)
A.“![]() ![]() | B.“![]() ![]() |
C.“![]() ![]() | D.“![]() ![]() |
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9卷引用:2024年高考全国甲卷数学(理)真题
2024年高考全国甲卷数学(理)真题专题05平面向量与复数专题03集合与常用逻辑(第三部分)(已下线)平面向量-综合测试卷B卷(已下线)2024年高考全国甲卷数学(理)真题变式题6-10(已下线)三年全国理科专题01集合、常用逻辑与不等式(已下线)五年全国理科专题01集合与常用逻辑(已下线)2024年高考数学真题完全解读(全国甲卷理科)(已下线)第02讲 常用逻辑用语(五大题型)(讲义)
名校
解题方法
2 . 在空间解析几何中,可以定义曲面(含平面)
的方程,若曲面
和三元方程
之间满足:①曲面
上任意一点的坐标均为三元方程
的解;②以三元方程
的任意解
为坐标的点均在曲面
上,则称曲面
的方程为
,方程
的曲面为
.已知空间中某单叶双曲面
的方程为
,双曲面
可视为平面
中某双曲线的一支绕
轴旋转一周所得的旋转面,已知直线
过C上一点
,且以
为方向向量.
(1)指出
平面截曲面
所得交线是什么曲线,并说明理由;
(2)证明:直线
在曲面
上;
(3)若过曲面
上任意一点,有且仅有两条直线,使得它们均在曲面
上.设直线
在曲面
上,且过点
,求异面直线
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fa13f27f92b55bd7ecd9d750f98ae99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1277d620abbfa26fb39600e53e606d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eedd047376c4cf1b9992cd8e4fe20df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d96461d2b3421aed548b754637ca8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d7a5b312e3d789a1070000315d63b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d0d16a4e8cc77c0433abc88df0a4a3.png)
(1)指出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2beb91f10d2d8f2aa0dcc3f5cd1598.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)若过曲面
![](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/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ddad9072eb1393ce15ca0627c941b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
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名校
解题方法
3 . 已知
,平面内动点
满足直线
的斜率之积为
.
(1)求动点
的轨迹方程;
(2)过点
的直线交
的轨迹
于
两点,以
为邻边作平行四边形
(
为坐标原点),若
恰为轨迹
上一点,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d7fae066efa772e21142aef5f764018.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec8858389f4c3156a946ba8bf0d8a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/459c84c9addfbd1cdd0a877ba7c584e4.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a5e484dfef494d27bc35ae7b8cf75d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ea16ceca816f7d3d50650af141baf42.png)
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4 . 命题“
”的否定是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f1b4c3a6c4e40b6bb6002ebf5e53fdc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 若向量
,
,
共面,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e938912144c782fb3e95af300eb3e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5708786412d7a989b1d8e1356f045e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df0f25b0b1742d6b0c0d9e42382fa4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f3cb8d72bb2e281b943b3b430138ef7.png)
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6 . 有下列四个命题:
(1)已知A,B,C,D是空间任意四点,则
;
(2)若两个非零向量
与
满足
,则
;
(3)分别表示空间向量的有向线段所在的直线是异面直线,则这两个向量不是共面向量;
(4)对于空间的任意一点O和不共线的三点A,B,C,若
当
时,(x,y,
),则P,A,B,C四点共面.
其中正确命题的个数是( )
(1)已知A,B,C,D是空间任意四点,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95e26118630b1ad0e3746c7ab1985830.png)
(2)若两个非零向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc1070a28cb9cb8553c29747d1993b16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b19f09e31d95863882d960637bdee63d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7612addf7073624b7d0e21a2ced44b2.png)
(3)分别表示空间向量的有向线段所在的直线是异面直线,则这两个向量不是共面向量;
(4)对于空间的任意一点O和不共线的三点A,B,C,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a8d49bf33e578b25811e22e26dbf584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd24c686fbaaa68705d654b880481ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/525c1a68848e95e6b419e0bbec3c0957.png)
其中正确命题的个数是( )
A.3 | B.2 | C.1 | D.0 |
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7 . 已知空间向量
,
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e58d1cd421cdf5fb7baa3fe205853a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce07fab1fc711a0802656035105acd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ead4767424866f1453c464a93b3ca8fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
A.![]() | B.3 | C.![]() | D.2 |
您最近一年使用:0次
名校
8 . 如图所示,三棱柱
中,
分别为棱
的中点,
分别是棱
上的点,
.![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
平面
;
(2)若三棱柱
为正三棱柱,求平面
和平面
的夹角的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/450176ba93397527fc3520c55dd1476a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95c0160e73beb94a4a1cbc0168e9a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e80c9702720a88f4a31c0484c7ff5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
(2)若三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6261790c66cc71ee3898afabad0c09f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
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名校
解题方法
9 . 抛物线
上的动点
到直线
的距离最短时,
到
的焦点距离为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c608def11fa0e2b34f05592ef1d11fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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10 . 点
为等轴双曲线
的焦点,过
作
轴的垂线与
的两渐近线分别交于
两点,则
的面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f2e83c2e45e771c25adcb58d8475559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ebaa32f4f1f4f807ca9aeb7fb29951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
A.![]() | B.4 | C.![]() | D.8 |
您最近一年使用:0次