1 . 如图所示的几何体中, ,
平面
,且
平面
,正方形
的边长为2,
为棱
中点,平面
分别与棱
交于点
.
(Ⅰ)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711aee9de6f59f725beb3dc0648a48a4.png)
(Ⅱ)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c19ac59727b522b2854176871a9ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
(Ⅲ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abf80148409afb32ced0b4f59f1ba709.png)
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11-12高二上·江西宜春·阶段练习
2 . 如图,已知向量
,可构成空间向量的一个基底,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4dceb16009db466f96b2d2c1b299d8.png)
,在向量已有的运算法则的基础上,新定义一种运算
,显然
的结果仍为一向量,记作
.
![](https://img.xkw.com/dksih/QBM/2011/12/14/1570613901074432/1570613906800640/STEM/68a97dfc-0465-4c43-b0f3-3e1f2b0da236.png?resizew=173)
(1)求证:向量
为平面
的法向量;
(2)求证:以
为边的平行四边形
的面积等于
;
(3)将四边形
按向量
平移,得到一个平行六面体
,试判断平行六面体的体积
与
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f54d5e324c4a3d08481cbf26e7f361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4dceb16009db466f96b2d2c1b299d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fc29483e99ae14302fbf12964a9de6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd8e4b39343d2c1557a4210aa4f757bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6c13f0f2b3b3ef5981d7fa3ff7f6b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fcc07589519bc2dfdc579585998323.png)
![](https://img.xkw.com/dksih/QBM/2011/12/14/1570613901074432/1570613906800640/STEM/68a97dfc-0465-4c43-b0f3-3e1f2b0da236.png?resizew=173)
(1)求证:向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20fcc07589519bc2dfdc579585998323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
(2)求证:以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d071d008cdc313f6ed16a602f8a9669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b76ac232477ac6d4b0a36eded969d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03bdc808dfcabe5199b3f3f98594b9b3.png)
(3)将四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b76ac232477ac6d4b0a36eded969d68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebca14060caa173dd7c922c560689064.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c89ef3197505169e99f933fab8ff7b83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcee40a45579d8c52db09dcd330d31c.png)
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