名校
解题方法
1 . 如图,已知正三棱柱
的底面边长为1,侧棱
的长为2,E、F分别为
和AC中点,则直线EF与平面
所成角的余弦值为______ ,异面直线
与
所成角的余弦值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
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2 . 如图所示,在正方体
中,
与
所成的角为________ ,
与
所成的角为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8cfbc0b5a8fbde804bd8425a4b76d207.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fbafedc202bd0d86c4dfdece9f8f4fe.png)
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名校
解题方法
3 . 已知正四棱锥
的所有棱长都为2,点
在侧棱SC上且
,过点
且垂直于SC的平面截该棱锥,得到截面多边形
,则
的边数为__________ ,
的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faeb97acf19bd3b2c6c77c2814df4d2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a45731695b5b3a1b0ff45dac9b210e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
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4 . 如图,已知长方体
中,
,
,
.
和
所成的角是_________ 度.
(2)
和
所成的角是_________ 度.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4746df85049d1651d3f6c30212a7a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/657d5471e57b894c3833bb3f43ff38ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24cfad1ba71a78d8f415335cde2f8c52.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6024fd4532f5f981deac4582c799a6ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e0f0ccc8492a0ccf1eee24867060643.png)
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2024·全国·模拟预测
5 . 在正四棱锥
中,点
分别为
的中点,
,异面直线
所成角的余弦值为
,则正四棱锥
的高为___________ ,外接球的表面积为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e7344dca1e40bf072371ddd5640111.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/080ca48cd27d4bf9d9ef084b558fc17a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db93ec2a531a5f1baa9cb243e46bf083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a6b832d2922f5c5fea6a1143250f70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
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2024高一下·全国·专题练习
6 . 棱长为3的正四面体
中,E,F分别是
和
的重心,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a71a9d21f77e9535de152bb33f802bb.png)
______ ,
与
的位置关系为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/891579e7c231584a8e16b8eeff79888e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ac451db3443cabb204f96c31fd4a02e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a71a9d21f77e9535de152bb33f802bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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7 . 如图,在正三棱锥
中,侧棱
,过点
作与棱DB,DC均相交的截面AEF.则
周长的最小值为_______________ ,记此时
的面积为
,则
N_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4357d5744046d4d44abb09e1ee35fcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5158a6e2e02f6b523fcb30b572390c60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/796b05775925f26408021b7ab2942dd9.png)
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名校
解题方法
8 . 如图1,菱形
的边长为
,
,将平面
、平面
同时绕BD向相对方向旋转,当A,C两点之间的距离等于BD时,构成四面体
,如图2所示,则BD与AC所成角的大小为________ ,四面体
外接球的表面积为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e46571701ccaa18d3c844ab99ee6c30e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7abd284f76d9f5769bc189508ce2572b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca67a5b8f69507c8b80379e86f90a8ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/9/c28a8229-dee0-4f73-a0d8-51bdf08c0a28.png?resizew=317)
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2024高三·全国·专题练习
解题方法
9 . 在长方体ABCDA1B1C1D1中,AB=AA1=2BC=2,则异面直线B1D1与CD的距离为________ ;异面直线BD1与CD的距离为________ .
您最近一年使用:0次
解题方法
10 . 如图,在正方体
中,
是棱
的中点,记平面
与平面
的交线为
,平面
与平面
的交线为
,若直线
分别与
所成的角为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ec7c99202b44d5d65239f65f155b6f.png)
__________ ,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5e3a0c883f301f42db9434be2cfd21.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2331bccb6ebf5b9fd639df994f575a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6426a6960d726b7378b7ceeb2f77b148.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3155cda6a054b2022df932f4e3364362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ec7c99202b44d5d65239f65f155b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c5e3a0c883f301f42db9434be2cfd21.png)
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