24-25高二上·全国·课前预习
名校
解题方法
1 . 如图,在棱长为
的正方体
中,
为
的中点,
,
分别在棱
,
上,
,
.
的长.
(2)求
与
所成角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038611b6f26e2c1a8cc6aee90f881203.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86c5baa19e466196686651467151ad4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c54dc0ff58e8c7d1035c2dff8572b30f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1dd5a3f83a7455eb3630364397accc.png)
您最近一年使用:0次
2023-08-25更新
|
919次组卷
|
6卷引用:河北省邯郸市武安市第三中学2023-2024学年高二上学期开学考试数学试题
河北省邯郸市武安市第三中学2023-2024学年高二上学期开学考试数学试题人教A版(2019)选择性必修第一册课本例题1.3 空间向量及其运算的坐标表示四川省成都市新津区成外学校2023-2024学年高二上学期10月月考数学试题四川省雅安市天立教育集团2023-2024学年高二上学期期中数学试题(已下线)1.3.2空间向量运算的坐标表示(导学案) -【上好课】高二数学同步备课系列(人教A版2019选择性必修第一册)(已下线)专题05用空间向量研究距离、夹角问题(2个知识点6种题型1个易错点1种高考考法)(3)
2 . 判断正误:
(1)已知向量
是空间的一组基,则向量
也是空间的一组基;( )
(2)若空间中的O,A,B,C四点不共面,则向量
是空间的一组基.( )
(1)已知向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5401d7f4a297c8b097e74bdebaaa8570.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1525cfabc81dd4d80e2f6154c3c864.png)
(2)若空间中的O,A,B,C四点不共面,则向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639cdeadbc9e566f81d65a0506823b80.png)
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3 . 在正方体
中,点E,F分别是底面
和侧面
的中心.求证:
(1)
平面
;
(2)
平面
;
(3)平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88e69074c44ab2ef7c46b7a4ee1c1ddf.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d1f6daed7a89d2c7aee5dd8f2d1ac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd148d264bc9043396f777523e907aa.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f9d682e5d3cc8573574d8d11636758.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd148d264bc9043396f777523e907aa.png)
(3)平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d9dc3b0398098f42398108fb181a91d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd148d264bc9043396f777523e907aa.png)
您最近一年使用:0次
解题方法
4 . 如图,在四棱锥
中,底面ABCD为直角梯形,
,
平面ABCD,
,
,
,求:
(2)二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/666c7e13a7999bd5970c1e478a665935.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c45fbffb9e2c7fa7c5006cde8da0cabe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91ce0586aafd9bf4fb7e1be082624afc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8365271d3239f07360fb71e86a8cc3ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0d5a2cd05e4476fc72271e8fdb59a9a.png)
(2)二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1636b4530c0b42d0e0b649e90e3b9e85.png)
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解题方法
5 . 如图,已知棱长为
的正四面体ABCD,点
,
,
分别是
,
,
的中点,求下列向量的数量积:
(1)
;
(2)
;
(3)
;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/28/f56baf20-98be-49e0-9c88-db7a9de6a0f1.png?resizew=181)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a47b376264d525c790ebad49a849c08.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21bfe273ec30b01f3245dfbf78b15083.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56aaa042299f80c1f135499e6855a1f9.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dfbe48e1b5e6d747134bbf9ff0a97a.png)
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6 . 如图,已知动圆M与两个定圆
和
分别外切,则动圆圆心M的轨迹是什么图形?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0385df6c7f8ee7ab503b6ed35933695b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cd73875650e1538c4c61d5e16d3db29.png)
您最近一年使用:0次
7 . 能否从图形的直观分析中判断出直线
:
与椭圆C:
的交点个数?若存在交点,则求出交点坐标;若不存在交点,则求椭圆C上的点到直线l的最小距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a362b22d77130726c8dda391382eb186.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
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8 . 化简:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ca58397a6ed24f757bf31b5abf5ddfe.png)
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9 . 如图,长方体
中,点E,F分别是
和BD的中点,
,
,
,将下列两组中相等的向量连线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08b344a0ebe520f4147702257aa276b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc9a915b6183ce6418229dad5fec617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f639828509b293069c2782d049d22f7.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/3a5ad65006ab94c402084227f4675b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3907ea50b201825d7a9cb46914e6c7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e08b344a0ebe520f4147702257aa276b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6791fcc6d52c804b82df1c6a0042ec34.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d021a5c98388463d577675e58068aa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef414b968b46ae08a9abde98cf9b50b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bc9a915b6183ce6418229dad5fec617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8e57fb5fe4b5757bcfa520db130562.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae54940f33b8714da5fe3b7546f8b3dc.png)
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解题方法
10 . 求下列双曲线的实轴和虚轴的长、顶点的坐标、离心率和渐近线方程,并画出双曲线的草图:
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f8ae565db8a7d4b95fdd85e28afa2f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b47e9edbf57fa31cb275a162d371780.png)
您最近一年使用:0次
2023-10-09更新
|
161次组卷
|
3卷引用:北师大版(2019)选择性必修第一册课本习题第二章2.2 双曲线的简单几何性质
北师大版(2019)选择性必修第一册课本习题第二章2.2 双曲线的简单几何性质(已下线)专题12 双曲线的几何性质8种常见考法归类(1)北师大版(2019)选择性必修第一册课本例题2.2 双曲线的简单几何性质