1 . 在空间直角坐标系
中,画出下列各点:
,
,
,
,
,
,
,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/085f68fdcbbda6b555a9c3436931cab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a62aea996509d673117cda86273ffc8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd4bb8d85ca045e48340fdfffd47f790.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/129492dfa12f575878876fdae59056f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1248bfbf7b6bfb975c9b1218e173cca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a74351a4978b08840453f6fa526bbbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaf5d80e612373e00ec7e84afdb7235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9db0256d136ece7f83319f78bd3c233.png)
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24-25高二上·全国·课前预习
2 . 判断正误,正确的画“正确”,错误的画“错误”.
(1)空间直角坐标系中,在
轴上的点的坐标一定是
的形式. ( )
(2)空间直角坐标系中,在坐标平面Ozx内的点的坐标一定是
的形式. ( )
(3)关于坐标平面Oyz对称的点其横坐标、纵坐标保持不变,竖坐标相反.( )
(4)若点A的坐标为
,则
.( )
(1)空间直角坐标系中,在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46c1d874c3dc0c93540dcb620dff010.png)
(2)空间直角坐标系中,在坐标平面Ozx内的点的坐标一定是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdb578300136814a37c0ea0199f77d5e.png)
(3)关于坐标平面Oyz对称的点其横坐标、纵坐标保持不变,竖坐标相反.
(4)若点A的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d685c54089867c395a4c49ba01b1237.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677b897e9b74cb2286a6df2fbe34f3fc.png)
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名校
解题方法
3 . 已知正方体
的棱长为2,点P为线段
上的动点,则点P到直线
的距离的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2023-10-10更新
|
636次组卷
|
5卷引用:四川省绵阳南山中学2023-2024学年高二上学期10月月考数学试题
4 . 在长方体
中,已知
,
,
.
的坐标;
(2)求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7479255f54d51b97e6314db1dc06eb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7d52fd1bdfe4ed2f1dc275b84a599e1.png)
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名校
5 . “十字贯穿体”是学习素描时常用的几何体实物模型,图1是某同学绘制“十字贯穿体”的素描作品.“十字贯穿体”是由两个完全相同的正四棱柱“垂直贯穿”构成的多面体,其中一个四棱柱的每一条侧棱分别垂直于另一个四棱柱的每一条侧棱,两个四棱柱分别有两条相对的侧棱交于两点,另外两条相对的侧棱交于一点(该点为所在棱的中点).若该同学绘制的“十字贯穿体”由两个底面边长为2,高为
的正四棱柱构成,在其直观图中建立如图2所示的空间直角坐标系
,则点
的坐标为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2023-10-05更新
|
139次组卷
|
3卷引用:河北省邢台市四校质检联盟2023-2024学年高二上学期第一次月考数学试题
河北省邢台市四校质检联盟2023-2024学年高二上学期第一次月考数学试题河北省邢台市河北南宫中学2023-2024学年高二上学期第一次月考数学试题(已下线)高二数学上学期期中模拟卷02(前三章:空间向量与立体几何、直线与圆、圆锥曲线)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)
6 . 在空间直角坐标系中,描出下列各点:
(1)
;
(2)
;
(3)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dc5818344df67b1a09540a891facefd.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b568563857fe7d3b7a0d45337264d2f0.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00afa7f5dd32415883fa4e976fd541d4.png)
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7 . 长方体
的长、宽、高分别为
,
,
.建立适当的空间直角坐标系,并求顶点A,B,C,D,
,
,
,
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ed9d97b8745ed1c15349ea3fffc299.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278c0760ffb04a907cddd8760d852b1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9b0c93c4275a7f5265c9ac8cb262c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3953cec61ac602ce5eb59b7912352179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3bd5e6bc2a0a277d279bb01af9584.png)
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8 . 如图,已知长方体
的棱长
,
,
.以点D为原点,分别以
,
,
为x轴、y轴、z轴的正方向,并均以1为单位长度,建立空间直角坐标系,求下列直线的一个方向向量:
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc11331a7b2d2619b40ee6d34c3bd620.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd21a4e45dc1beb069d7e78f84a51544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a754ad0537577221e7be168127d7cba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c085dbb9d78aef7d81c3f4d6855f067b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64464499f7e3330250ee06b939a5e4ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b435d7fc33860ae191f9111d880b40.png)
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9 . 如图长方体
中,
分别是
的中点,如图所示建系,则
中点的坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48eb419428729b96a728161edac52c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f5e467a47bc0271e4907f5f77b52658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/13/2da71a85-fc9f-41f4-a0eb-2c1a5250a256.png?resizew=167)
A.![]() | B.![]() |
C.![]() | D.![]() |
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10 . 如图所示,已知直三棱柱
中,
,且D,E分别是棱
的中点.建立适当的空间直角坐标系,求
与
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc3da31308939249b9659f19d81c960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea4dfea6353fc25e88535e865a4982cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
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