1 . 在四棱锥
中,底面
是边长为
的菱形,
,
.
(I)证明:
平面
;
(II)若
,求二面角
的余弦值.
![](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/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e075468e7fb0bf30229aec01a7205977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851cf6b3cb9b2486771a0d69ae47c678.png)
(I)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(II)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b80ee363635d73f601654339028daec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad6a0cee8226e82cc57916e10d533369.png)
![](https://img.xkw.com/dksih/QBM/2018/4/24/1931033716408320/1936081014661120/STEM/c7aad0e8c7524bfb8d83cd6855840c79.png?resizew=162)
您最近一年使用:0次
2017-02-08更新
|
1113次组卷
|
7卷引用:新疆克拉玛依市2022届高三第三次模拟检测数学(理)试题
解题方法
2 . 如图,在直三棱柱
中,
是正三角形,
是棱
的中点.
![](https://img.xkw.com/dksih/QBM/2017/4/23/1671982603296768/1675064833654784/STEM/45864119060e4498a5ed92dde6a4306f.png?resizew=171)
(1)求证:平面
平面
;
(2)若
,求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://img.xkw.com/dksih/QBM/2017/4/23/1671982603296768/1675064833654784/STEM/45864119060e4498a5ed92dde6a4306f.png?resizew=171)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3837007567ab66f5cbe93ea39d6b259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac61c24f99a4e466f1e2ea011893866.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeed487430a5b8a330f2d0c52166521a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b43d2e0874d9d1ae0d9b237d5924554.png)
您最近一年使用:0次
3 . 如图,在直三棱柱
中,
,
,
分别是
的中点.
![](https://img.xkw.com/dksih/QBM/2015/5/21/1578657684332544/1578657684873216/STEM/941dbe00e1d24bc7bf4309ae533656a2.png)
(1)求证
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57f47d6a88e962cd790d2f159c021ec1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31d834844ba3b70d4aa6262163800a35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb717228e1762d335814a3adc90eae45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d92ab2e616111dbe7b501161e75ecaba.png)
![](https://img.xkw.com/dksih/QBM/2015/5/21/1578657684332544/1578657684873216/STEM/941dbe00e1d24bc7bf4309ae533656a2.png)
(1)求证
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5930a6d5394e6cdb6b89cf6c18dc1fb.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/249c841f2d649424b8a019055da7e0c8.png)
您最近一年使用:0次
4 . 如图,三棱锥
中,
是正三角形,
平面
,
,
为
中点,
,垂足为
.
![](https://img.xkw.com/dksih/QBM/2016/4/6/1572566745825280/1572566752026624/STEM/421e609026924f248f19cf77e5427b36.png?resizew=208)
(1)求证:
;
(2)求二面角
的平面角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f1897a7e856b42f8cee0f286ad913d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2c9c32921b9f678056406dbb27fd9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53d1e3701b45f028de14ae8166c75c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://img.xkw.com/dksih/QBM/2016/4/6/1572566745825280/1572566752026624/STEM/421e609026924f248f19cf77e5427b36.png?resizew=208)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae20968d87623467882df2b5c2ceab1.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed7a8116d2f02b52c33fb7a49fc0d1ae.png)
您最近一年使用:0次
2016-12-04更新
|
452次组卷
|
2卷引用:2016届新疆乌鲁木齐地区高三第二次诊断性测验理科数学试卷
5 . 在平面直角坐标系
中,动点
到点
的距离比它到
轴的距离多1.
(Ⅰ)求点
的轨迹
的方程;
(Ⅱ)过点
任作直线
,交曲线
于
两点,交直线
于点
,
是
的中点,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/055a2ef09e2ee0948cf67c58de58732d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(Ⅰ)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff32df158dd2d590af5646657afb0101.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/145ef2d91a57e6ea189c0cf1232e81c3.png)
您最近一年使用:0次
2016-12-04更新
|
1635次组卷
|
2卷引用:2016届新疆乌鲁木齐地区高三第二次诊断性测验理科数学试卷
2010·辽宁·一模
6 . 如图所示的多面体,它的正视图为直角三角形,侧视图为矩形,俯视图为直角梯形(尺寸如图所示)
(1)求证:AE//平面DCF;
(2)当AB的长为
,
时,求二面角A—EF—C的大小.
![](https://img.xkw.com/dksih/QBM/2011/3/29/1570085586083840/1570085591171072/STEM/cdd4a667e2f34d0babb77c858d577531.png?resizew=239)
![](https://img.xkw.com/dksih/QBM/2011/3/29/1570085586083840/1570085591171072/STEM/b33953b57e1449a5af4ec29f4c3b348f.png?resizew=304)
(1)求证:AE//平面DCF;
(2)当AB的长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0874f019492261eb175bdcc08c189d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db111a217e7d3313f77a68be312d552b.png)
![](https://img.xkw.com/dksih/QBM/2011/3/29/1570085586083840/1570085591171072/STEM/cdd4a667e2f34d0babb77c858d577531.png?resizew=239)
![](https://img.xkw.com/dksih/QBM/2011/3/29/1570085586083840/1570085591171072/STEM/b33953b57e1449a5af4ec29f4c3b348f.png?resizew=304)
您最近一年使用:0次
2010·辽宁·一模
7 . 已知椭圆
左、右焦点分别为F1、F2,点
,点F2在线段PF1的中垂线上.
(1)求椭圆C的方程;
(2)设直线
与椭圆C交于M、N两点,直线F2M与F2N的倾斜角分别为
,且
,求证:直线
过定点,并求该定点的坐标.
![](https://img.xkw.com/dksih/QBM/2010/8/6/1576721184817152/1576721252155392/STEM/feef9ef6d88342d8a41aca7dd7a6428f.png)
![](https://img.xkw.com/dksih/QBM/2010/8/6/1576721184817152/1576721252155392/STEM/ea6cc896f4ac4ad6b7e46efa5d161b45.png)
(1)求椭圆C的方程;
(2)设直线
![](https://img.xkw.com/dksih/QBM/2010/8/6/1576721184817152/1576721252155392/STEM/135746207f7e4b46b97c2d76642b4218.png)
![](https://img.xkw.com/dksih/QBM/2010/8/6/1576721184817152/1576721252155392/STEM/df72f957235644afbca0f5c5568f8db3.png)
![](https://img.xkw.com/dksih/QBM/2010/8/6/1576721184817152/1576721252155392/STEM/8803442a916f44a3ab2063ae19713768.png)
![](https://img.xkw.com/dksih/QBM/2010/8/6/1576721184817152/1576721252155392/STEM/e96e0ca3dc0249bca56e60d4210b5aac.png)
您最近一年使用:0次