名校
1 . 如图,在直三棱柱
中,
是棱BC上一点(点D与点
不重合),且
,过
作平面
的垂线
.
;
(2)若
,当三棱锥
的体积最大时,求AC与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9d2462e6dbd321cf3abae25a56adf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bcc3c5b41a01362779683f5b70710c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/446091491fb55549972f35a206fcab1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5445220e9b81a876e359615859a5a58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ba9e20d667d04bf3ee7f55cc795ce01.png)
您最近一年使用:0次
昨日更新
|
297次组卷
|
3卷引用:海南省2022-2023学年高二下学期学业水平期中考试数学试题
名校
解题方法
2 . 如图,在四棱锥
中,
平面
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
平面
,底面
为矩形,点
在棱
上,且
与
位于平面
的两侧.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/3bb6f445-bcb3-4ca1-9d3f-a3405aaf77e1.png?resizew=206)
(1)证明:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
平面
;
(2)若
,
,
,试问在线段
上是否存在点
,使得
与
的面积相等?若存在,求
到
的距离;若不存在,说明理由.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1633988fd62a652de726ee92a917b52d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/6/3bb6f445-bcb3-4ca1-9d3f-a3405aaf77e1.png?resizew=206)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/638537c0a30676c73fea76c80e0f8bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/985d0ad3196bf9d13baced16572fbf95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6370d6c626bdabf1fc694501ee6c714f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fb6e81fee5674c3e26a65e58cc506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb49df05f2e31d005735c3f14a21d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
您最近一年使用:0次
2023-01-30更新
|
1208次组卷
|
3卷引用:第03讲 空间中平行、垂直问题10种常见考法归类(1)
(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(1)河南省开封市2022-2023学年高三上学期1月期末联考数学试题(文科)重庆市第一中学教育共同体2022-2023学年高一下学期期中数学试题
20-21高二上·江苏南通·期中
3 . 如图,在平面四边形DACB中,
,
,
,现将
沿AB翻折至
,记二面角
的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/3b4bb8cc-cb12-45e0-a191-5532555d2afa.png?resizew=233)
(1)求证:
;
(2)当
时,求直线
与平面ABC所成的角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c863257d994bee7b39c9e0b5ce8ea37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38e15db76bb6a4abbf5522e1f975dc27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f08273d339dc5ddbb89aa67bb8205e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd4c625a55ef1d2920a0605d52c8da23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d29c9fdc9016fe5ebdf8fa4019969a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cd606081fe85a262777717651cabb82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d579f10d1cfc46f35a54dd51da15aa64.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/18/3b4bb8cc-cb12-45e0-a191-5532555d2afa.png?resizew=233)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb936d24d3237261a7198e6a70f1a456.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72bf0fce80daad394f2a9d013829c5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8b40d14544a9be0bebdb276f0fa865.png)
您最近一年使用:0次
解题方法
4 . 如图几何体是圆锥的一部分,它是Rt△ABC(及其内部)以一条直角边AB所在直线为旋转轴旋转150°得到的,AB=BC=2,P是弧
上一点,且EB⊥AP.
![](https://img.xkw.com/dksih/QBM/2020/1/13/2376306543706112/2422032537239552/STEM/fb28e887-8993-453a-9faf-95b326072086.png)
(1)求∠CBP的大小;
(2)若Q为AE的中点,D为弧
的中点,求二面角Q﹣BD﹣P的余弦值;
(3)直线AC上是否存在一点M,使得B、D、M、Q四点共面?若存在,请说明点M的位置;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3839ab58dabbf4c12ee69770bdbf8dac.png)
![](https://img.xkw.com/dksih/QBM/2020/1/13/2376306543706112/2422032537239552/STEM/fb28e887-8993-453a-9faf-95b326072086.png)
(1)求∠CBP的大小;
(2)若Q为AE的中点,D为弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67a4fdec4ee1fc83fdd6b4c324755d95.png)
(3)直线AC上是否存在一点M,使得B、D、M、Q四点共面?若存在,请说明点M的位置;若不存在,请说明理由.
您最近一年使用:0次