23-24高二上·上海·课后作业
解题方法
1 . 如图,在直三棱柱
中,
,
,棱
,点
、
分别是
、
的中点.建立适当的空间直角坐标系,解决如下问题:
(1)求
的模;
(2)求
;
(3)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae445b17e686495b7ef5783c83c96410.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a3cc9cccfb4c260dac05f4ed57e8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4acc5d21a7490e6bed2453cc5147c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a696a182fff038a86b2bbe8ca099442.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/14/4a12667b-b2bc-4aea-b5c7-4068e55ddf8f.png?resizew=105)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350f162ee9aa08f4c9779481a5ef1025.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8732e96e02aa9a706af3f0dc4c6796.png)
(3)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b201f1e798eb74963b98f2b0da4132.png)
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解题方法
2 . 设常数
.在棱长为1的正方体
中,点
满足
,点
分别为棱
上的动点(均不与顶点重合),且满足
,记
.以
为原点,分别以
的方向为
轴的正方向,建立如图空间直角坐标系
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/e06e4e4f-445b-442f-8e80-1e0f640affc9.png?resizew=217)
(1)用
和
表示点
的坐标;
(2)设
,若
,求常数
的值;
(3)记
到平面
的距离为
.求证:若关于
的方程
在
上恰有两个不同的解,则这两个解中至少有一个大于
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eb6bf23a5a12e1ba5413594d7b1a57c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a91c73ae980263c97742283b6b5852a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cea77ba313fcc751481ac1ca214df3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e85b55b6ad43be1a03fc637e1d3429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651066b6919cab279373a8a1e1130839.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d68873c59a21b0cd408cdf2b47d51096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a14c388e1e2e5a2ff1ccf6caffbee0d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/13/e06e4e4f-445b-442f-8e80-1e0f640affc9.png?resizew=217)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15b268af571f9ecb37a864a08862814.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d262b77e692c60e3c6b6afb610e8fe66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c28b88046022376b082b8a45c04577c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a90170d7ef5ff6d1d63517c166f7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a19e72906b84a1cb049167afdebdce0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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3 . 如图,在四棱锥
中,
平面ABCD,
,
,
,
,E为PD的中点,点F在PC上,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/1748ab0f-33d4-4cad-8e56-a17ceb1aae3d.png?resizew=169)
求证:
平面PAD;
若平面AEF与线段PB交于点G,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb2dd10731b99c0f4f89ee957f8a239.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e0a957a55460c72673c0f2ee90dbb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52a923784f083b7f4777891afe06b44e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f88454ace46996b99361d18e76189cdc.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/1748ab0f-33d4-4cad-8e56-a17ceb1aae3d.png?resizew=169)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97f30533da2e1d2a958dc906c37eba9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f68b51d4182b15bbe2ff835264893f0.png)
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