题目
题型:不详难度:来源:
(Ⅰ)如图1,
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123933-65484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123933-74682.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123934-14196.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123934-75730.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123934-81374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123934-17454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-77563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-10458.png)
(Ⅱ)如图2,设
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-85749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-82969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123936-72254.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-85749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123934-17454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123936-49955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123936-49244.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123936-88567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123937-57652.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123937-56429.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123937-44696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123937-11429.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123938-13750.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123934-81374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123934-17454.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123938-52820.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-10458.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-85749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-82969.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123938-97478.png)
分别得出向量
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123938-37380.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123939-61555.png)
解:(Ⅰ)由于
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123933-65484.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-77563.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123938-52820.png)
即
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123939-73881.png)
化简为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-10458.png)
结论得证. ………7分
(Ⅱ)连结
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123939-97591.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-85749.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123935-82969.png)
所以:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123939-42763.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123936-88567.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123937-57652.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123940-83493.png)
由(Ⅰ)知:
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123940-78374.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123938-13750.png)
核心考点
试题【(本小题满分15分)(Ⅰ)如图1,是平面内的三个点,且与不重合,是平面内任意一点,若点在直线上,试证明:存在实数,使得:.(Ⅱ)如图2,设为的重心,过点且与、(】;主要考察你对空间向量的线性运算等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123926-98670.png)
(1)若
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123926-94191.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123926-65513.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123926-23575.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123926-20100.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123927-86614.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123927-72954.png)
(2)试求实数k的值,使向量
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123927-40930.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123927-33420.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123914-54080.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123914-82705.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123915-53824.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123915-57557.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123915-95167.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123915-59518.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123916-34719.jpg)
A.![]() | B.![]() |
C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123907-74514.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123908-73569.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123908-29931.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123908-59470.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123908-60562.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123909-40350.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123909-71774.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123901-24980.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123901-55650.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123901-65771.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123901-27364.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123902-52218.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123902-15423.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123902-79809.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123903-86626.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123903-83181.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123857-31629.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191105/20191105123857-46641.png)
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