如图,在空间直角坐标系中有直三棱柱
,点A,B分别在x轴、y轴上,
,平面
的一个法向量为
.
(1)求点
与
的坐标;
(2)求点O到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a60f5d069760bfe69f9cdc1b6e1e048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b32ab04dd852329d5918b177c199eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3da630440d6d416f19ee22c8431c882.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a010e3cb3ceff17865af1d2d16833e36.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/15/91c34dd7-3590-419b-89b1-081936c8898d.png?resizew=137)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f919bd3dde10dbbc076f7ec5149699.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)求点O到平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3da630440d6d416f19ee22c8431c882.png)
更新时间:2023-09-30 11:28:57
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解答题-问答题
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【推荐1】已知
.
(1)写出直线
的一个方向向量;
(2)设平面
经过点
,且
是
的一个法向量,
是平面
内任意一点,试写出
满足的关系式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7482f5873fe656fd96589354b783a2.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(2)设平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89265cbe3abc6b966ce8967fead448b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c221d2664017226eb27ac2468fb2e97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
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【推荐1】如图,在直三棱柱ABC—A1B1C1中,△ABC是边长为2的正三角形,AA1=2
,D是CC1的中点,E是A1B1的中点.
![](https://img.xkw.com/dksih/QBM/2020/11/6/2587377121984512/2588075600494592/STEM/a4f71e746f7f48739f2d8c7ea01c49eb.png?resizew=241)
(1)证明:DE∥平面A1BC;
(2)求点A到平面A1BC的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
![](https://img.xkw.com/dksih/QBM/2020/11/6/2587377121984512/2588075600494592/STEM/a4f71e746f7f48739f2d8c7ea01c49eb.png?resizew=241)
(1)证明:DE∥平面A1BC;
(2)求点A到平面A1BC的距离.
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【推荐2】如图,在四棱锥
中,底面
是矩形,且
底面
,
,若
且
.
的值;
(2)若
平面
,求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26d6fc4687ab74c8a24278153dfe014c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5078d2a4af999f9e38d9e4207beb2dd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac559a1a89bfb16e1c44cdd7ad2f2bbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1100379a4385b9ce064847bc21760adc.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b70cef0b79ca64acbb67dc667fc53b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
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