1 . 对于数集
,其中
,
,定义向量集
,若对任意
,存在
,使得
,则称
具有性质
.
(
)设
,请写出向量集
并判断
是否具有性质
.
(
)若
,且
具有性质
,求
的值.
(
)若
具有性质
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4622c700325a90d453e6300b886a8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bc1a0bba5e6e8ddf6f1f60f78e6490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8bfed73c13a4ba150b097d24fa9a0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7eaae85741a85ff6fceaf51d7b7c908c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffe6217f5a3a719f6a1ffbd4cb05dbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0e442b3e4354982f3f2b8e725b6e43c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66317f3834697e2b5642906bb751eb25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a829fdd8ec0f3b7ede883cf2c3e53b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0aa2ef928b6e3341d0a0dc6d8055b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9df99e7b8d91a016727f39ea5a39d8e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f022950e0faa45b617d497b01b5292b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551ee6e86b2c6e79236dfe3e2e2c24b.png)
您最近一年使用:0次
2 . 已知集合
对于
,
,定义A与B的差为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d3cda07e85dcc0f0abdd4009033185.png)
A与B之间的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e27c2552f93678beed8a2da09d9f82c.png)
(Ⅰ)证明:
,且
;
(Ⅱ)证明:
三个数中至少有一个是偶数
(Ⅲ) 设P
,P中有m(m≥2)个元素,记P中所有两元素间距离的平均值为
(P).
证明:
(P)≤
.
(考生务必将答案答在答题卡上,在试卷上作答无效)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d6a56fba87eb11270936ec057e58145.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9247eb1841878ba0f36a717a7c6f4d4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cccbf2256857847034bdd6e0bedcdd4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d3cda07e85dcc0f0abdd4009033185.png)
A与B之间的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e27c2552f93678beed8a2da09d9f82c.png)
(Ⅰ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe6617cee7f47ed6bb6d0291a8e75473.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70958c6e20ee298ce93e7eb4434a9206.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98e6deac71f097fe2ae7121691ac67e4.png)
(Ⅲ) 设P
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d57f40f7df91c9fc7992670d8d4bec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92751d41a1ec61f309b6a3f6032b731e.png)
证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92751d41a1ec61f309b6a3f6032b731e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8402e5be50a188507a4feb16ed56ea4d.png)
(考生务必将答案答在答题卡上,在试卷上作答无效)
您最近一年使用:0次
2016-11-30更新
|
552次组卷
|
4卷引用:北京市第一七一中学2021-2022学年高二上学期数学期中调研试题
北京市第一七一中学2021-2022学年高二上学期数学期中调研试题2010年高考试题北京(理科)卷数学试题(已下线)专题16 数列新定义题的解法 微点1 数列新定义题的解法(一)(已下线)第五篇 向量与几何 专题19 抽象距离 微点2 抽象距离——曼哈顿距离(二)
3 . 已知集合
对于
,
,定义A与B的差为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9494aad384d2bbd9f570f12c6fc31ee.png)
A与B之间的距离为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b53822fe6093b43b46beae65d6abe3.png)
(Ⅰ)当n=5时,设
,求
,
;
(Ⅱ)证明:
,且
;
(Ⅲ) 证明:
三个数中至少有一个是偶数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0062971d409798b8a716209536536f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3615fd277cc1be2d8d8468a1ab9e3e96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eddb6f1abafe3023e19e095346474f9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9494aad384d2bbd9f570f12c6fc31ee.png)
A与B之间的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23b53822fe6093b43b46beae65d6abe3.png)
(Ⅰ)当n=5时,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4660939da3ac24195b0a7b3773e9fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e9e460c144f7a2141d2df0308b125f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4a2681390214200443ae07c01a4abe.png)
(Ⅱ)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4010da33cf43870f86be1bf9bfd6d0e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8513f18376e4e456b939d0f1cdb6e602.png)
(Ⅲ) 证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f859a0d4fb5579ac99e061da9a8a6de1.png)
您最近一年使用:0次
2016-11-30更新
|
457次组卷
|
4卷引用:北京市丰台区第十二中学2021-2022学年高二上学期期中数学试题