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1 . 如图,已知:正方形ABCD边长为1,P是正方形ABCD的对角线BD上一点,四边形PFAE为矩形.建立坐标系用向量法证明:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/14/ede237f0-1e70-4e16-a608-735bfe69626f.png?resizew=148)
(1)
;
(2)
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/14/ede237f0-1e70-4e16-a608-735bfe69626f.png?resizew=148)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b16928cd1c2ff1971efce435d1930a78.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfa8355d95bb4c8d7c004eab4c7ce784.png)
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2 . 在平面直角坐标系
中,已知一列点:
,
,
,
,
,
,其中
,向量
.
(1)求
和
的值;
(2)证明:对任意的正整数
,都有
;
(3)若正整数
满足
,则下列结论中正确的有___________.(填入所有正确选项的序号)
①
;②
;③![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8847828c19ed125bc70b12d427b485.png)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3699abf2078c061894952528e6d9d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cdf35d502313b2efe577c1bfc4aa1e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac10857a95801d2f3a97d876c3365738.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3633f5e5e1fa6c0470d231d09902058.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e5531913e2f170465d8df01795cd51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29d5ec9ad92f37e64eccce922ab1b14e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60cfae860356f22ec6014204780d80a.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9304a8cfb0fcbbfae416a9e11021a497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72254fff7080ad8d573893cd00bd9387.png)
(2)证明:对任意的正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49769e8d151949dea6ac52a703ef0d2e.png)
(3)若正整数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4d7e68d0c8bd9a32d826c721ab74d9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22e517c32ed93de4d9cb6e0926337000.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4554216a40609d219999b89fb2096514.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fae599db039ed08f0f68baa2a21bfa5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8847828c19ed125bc70b12d427b485.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6087d579135b048189dd5b332ec46a7.png)
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2022-07-19更新
|
687次组卷
|
3卷引用:北京市东城区2021-2022学年高一下学期期末数学试题
北京市东城区2021-2022学年高一下学期期末数学试题(已下线)6.3.5 平面向量数量积的坐标表示(分层作业)-【上好课】2022-2023学年高一数学同步备课系列(人教A版2019必修第二册)第9章 平面向量(单元测试)-2022-2023学年高一数学同步精品课堂(苏教版2019必修第二册)
3 . 已知点
,点
为一次函数
图象上的一个动点.
(1)用含
的代数式表示
;
(2)求证:
恒为锐角;
(3)若四边形
为菱形,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c2773896cd546fb3b840a2604d3592.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e6e15daf7b14dbff32c390f4984dcfb.png)
(1)用含
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6983a471f24a61ef9ba49b814bf994c.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
(3)若四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/712d9d9e29645c1df6ae23125b4aa1cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2d68310668412a7fe7a6a063214370c.png)
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12-13高一上·北京·期末
4 . 已知:向量
,
,
.
(1)若
,求证:
;
(2)若
与
垂直,求
的值;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d57db085309d8e2ed98fb2049ecc4c42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ae8b0161424e113a3f4555d7bf47de9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/164afb4590e99ce11219cef8811a019c.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84daf014c0913d770ce7ec2c7f5da4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/076559f08d17fb25e82886e791719e52.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc9b91fb8d355f0aa521e0e45a63407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673f7e66c2a252da4c77c70d90c8cec.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0be60ba20ec289f46af9006919315b99.png)
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