题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-95337.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-68151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-52347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-42745.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-84560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-84560.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-41438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-55988.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-49802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-49802.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-49149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-74367.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-36714.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-25014.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-66985.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-34801.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-53999.jpg)
(1)设点
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-32543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-41043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-55975.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-41438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-49149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-75134.png)
(3)求平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-22423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-22920.png)
解析
试题分析:(1)将侧面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-46676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-40302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-41043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-38958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-32543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-49149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-55975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-91600.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-48404.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-41949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-48639.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-14671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-41438.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-49149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-75134.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-52347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-37286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-16791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-17041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112036-79633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112036-49536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112036-91602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112037-21071.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112037-95525.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
试题解析:(1)将侧面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-46676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-41043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-40302.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112037-41405.png)
则当
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-38958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-32543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-49149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-55975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-55975.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-91600.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112037-60221.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112037-69893.png)
在
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112038-68120.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112038-75235.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112038-36878.png)
在三角形
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112038-92921.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112039-29234.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112039-59422.png)
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112039-33964.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112040-75210.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112040-34556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112040-82517.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-46676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112040-87634.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-46676.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112040-47476.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112041-29194.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112041-27936.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-41949.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112041-76435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112034-41949.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112041-20795.png)
同理
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-14671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112042-66341.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112032-49149.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-75134.png)
(3)方法一:如图,以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112031-52347.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-37286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-16791.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112035-17041.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112036-79633.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112036-49536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112036-91602.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112042-18384.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112042-59435.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112043-71012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112043-45671.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112043-66226.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112043-78054.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112044-25305.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112044-15763.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112044-69656.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112044-36377.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112045-11288.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112045-11062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-22920.png)
方法二: 由
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112045-86598.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112045-71181.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112045-69182.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112046-61834.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112046-98060.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112046-62103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
设平面
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112046-81069.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112047-57482.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112047-86068.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112047-56280.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112048-82039.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112048-68586.png)
又
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112048-43914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112048-29516.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112049-87781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112049-61851.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112049-87781.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112049-95951.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112049-98576.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112050-28192.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112050-14336.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112050-58012.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112045-11062.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-58553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112030-12370.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112033-22920.png)
核心考点
试题【如图,四棱锥的底面是正方形,侧棱底面,过作垂直交于点,作垂直交于点,平面交于点,且,.(1)设点是上任一点,试求的最小值;(2)求证:、在以为直径的圆上;(3)】;主要考察你对空间向量的基本概念等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112015-15135.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112015-31669.jpg)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112015-68152.png)
(2)求二面角A-BP-D的余弦值.
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112002-44586.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112002-70647.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112002-56985.png)
(1)证明:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112003-70798.png)
(2)若二面角D1—EC—D的大小为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112003-83363.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105112003-93043.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111942-54479.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111943-21051.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111943-92536.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111943-69027.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111943-26083.png)
(1)求异面直线
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111944-41707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111944-30910.png)
(2)若二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111944-20143.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111944-13125.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111944-32837.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111945-58291.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111927-90711.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111927-79638.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111927-27556.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111927-26323.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111905-71077.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111905-58092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111906-95814.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111906-10232.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111906-67951.jpg)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111907-88469.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111907-23315.png)
(2)求二面角
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105111907-80102.png)
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