题目
题型:不详难度:来源:
(1)求证:平面PBC⊥面PDC
(2)设E为PC上一点,若二面角B-EA-P的余弦值为-
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-10430.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-89348.png)
答案
(2)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-69165.png)
解析
PB2=PA2+AB2-2AB·PAcos600=4+1-2×1×2×
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-64982.png)
∴PA2=PB2+AB2,即AB⊥PB
∵DA⊥面ABP,CB∥DA
∴CB⊥面ABP
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-82151.png)
又DC∥AB,∴DC∥面PBC
∵DC
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-40350.png)
(2)如图建立空间直角坐标系
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-68214.png)
则A(0,1,0),P(
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
设E(x,y,z),
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-89267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-11828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-89757.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-62286.png)
则(-
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-11828.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-82151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-62286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-62286.png)
设面ABE的法向量为n=(a,b,c),则
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-67849.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-82151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120927-24269.png)
令c=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-82151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120927-20219.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-82151.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120927-29724.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
同理可求平面PAE的法向量为m=(1,
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
∵cos<n,m>=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120927-12418.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120927-44933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120928-27503.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-10430.png)
∴
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-62286.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-64982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120926-62286.png)
∴E(
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120928-61669.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-64982.png)
∴VE-PAB=
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120928-40076.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-64982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120925-94784.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-64982.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120924-69165.png)
核心考点
试题【如图,四棱锥P-ABCD中,底面ABCD为正方形,DA⊥面ABP,AB=1,PA=2,∠PAB=60°.(1)求证:平面PBC⊥面PDC(2)设E为PC上一点,】;主要考察你对柱锥台的表面积等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-64355.png)
(1)试判断折叠后直线AB与平面DEF的位置关系,并说明理由;
(2)若棱锥E-DFC的体积为
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-87005.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-64355.png)
(3)在线段AC上是否存在一点P,使BP⊥DF?如果存在,求出
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-30827.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120912-40914.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120903-15262.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120903-32048.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120903-18263.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120905-91445.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-94958.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-30686.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-90361.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-35656.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-54445.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-76730.png)
(2)若
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-21885.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120858-87191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120859-63580.jpg)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-31103.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-78960.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-34662.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-93704.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-26260.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-25689.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120841-77366.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-24707.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-50353.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-33670.png)
(1)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-44249.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120842-94934.png)
(2)求证:
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120843-96048.png)
(3)求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120843-96705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120843-59171.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120830-78476.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-95972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-53216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-95972.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-86697.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-56900.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-85955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-93003.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-98254.png)
(1)作出这个几何体的三视图(不要求写作法).
(2)设
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-87272.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-37396.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-67881.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120831-93408.png)
(3) 求三棱锥
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120832-57216.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191021/20191021120832-50380.png)
最新试题
- 1Annie _______ to the party. She had a wonderful time with us
- 2当今世界,科技实力和创新能力越来越决定着各国在全球政治、经济舞台上的地位和尊严。为此,我国必须( )①实施科教兴国战
- 3下列有关东印度公司的说法错误的一项是[ ]A.它只有进行商业贸易的权利 B.19世纪早期,它统治了印度的大部
- 4一天当中,陆地最高气温一般出现在 ,最低气温出现在 ;一年当中,世界陆地上大多数地方的
- 5选出下列各项中成语使用恰当的一项:()A.主观主义者的滥调文章实属不刊之论。B.近期来,有些商家打着“买一赠一”的旗号欺
- 6【题文】已知集合为集合A的一个三元子集,设A的所有三元子集的元素之和是=
- 7通常作为人体储备的能源物质是( )A.糖 类B.维生素C.蛋白质D.脂 肪
- 8在0.02m2的物体表面上,受到压力是______时,物体表面受到的压强是200Pa.
- 92010年10月20日学习郭明义同志先进事迹座谈会在北京举行。郭明义,一个鞍钢普通职工的名字,在2010年逐渐传遍全国。
- 10_______ some ways , there are many changes in our hometown .
热门考点
- 1阅读下文。(13分)无价的奖赏①当她猛然发现身边的手提包不见了时,吓得冷汗涔涔。那手提包里的钱和银行卡都在。其次,关乎“
- 2如图,⊙O直径AB=4,点C,D是圆上两点,∠BDC=40°,则弧BC长为______.
- 3— ____? — No, thanks. I’m just looking around. I’ll let
- 4当m=( )时,关于x的方程(m+2)x﹣2=1﹣m(4﹣x)有正数解.
- 5一个静止的质量为M的原子核,放射出一个质量为m的粒子,粒子速度为v,则核剩余部分的速度为( )A.mv(M-m)B.-
- 6竖直升空的火箭,其v-t图象如图所示,由图可知以下说法中正确的是( )A.火箭上升的最大高度为16000mB.火箭上升
- 7下列有关同位素的说法正确的是A.电子数相同,中子数不同的两种微粒B.质子数相同,中子数不同的两种原子C.质子数相同,中子
- 8原命题:“设a、b、c∈R,若a>b,则ac2>bc2”.在原命题以及它的逆命题,否命题、逆否命题中,真命题共有____
- 9在如图所示的电路中,电源电压不变,电阻R1大于R2.闭合电键后,通过R1的电流I1与通过R2的电流I2的关系是( )A
- 10达尔文的自然选择学说不能解释的现象是[ ]A.生物的多样性 B.生物的适应性 C.生物进化的原因