已知在直角坐标系xOy中,P(1,1),A(x,0)(x>0),B(0,y)(y>0)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/be351de4-df5e-4bb7-ae99-4ae4d7b782b7.png?resizew=160)
(Ⅰ)若x=
,
⊥
,求y的值;
(Ⅱ)若△OAB的周长为2,求向量
与
的夹角.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/30/be351de4-df5e-4bb7-ae99-4ae4d7b782b7.png?resizew=160)
(Ⅰ)若x=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10402e4ddd0d323cc1ae83801ae976db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132f0b15fc19323ade9a92ec8ea5d70a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0db4603f3826a9e523ba01bbd609bef.png)
(Ⅱ)若△OAB的周长为2,求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09373a4f6329dc492aff9371352ded10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132f0b15fc19323ade9a92ec8ea5d70a.png)
更新时间:2019-01-15 15:53:28
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相似题推荐
解答题-问答题
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(0.4)
名校
【推荐1】已知向量
,单位向量
与向量
的夹角为
.
(1)求向量
;
(2)若向量
与坐标轴不平行,且与向量
垂直,令
.请将
表示为
的函数
,并求函数
的定义域和最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91a234421f2ea6e6b07f20d5aede234c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184c6736108865aa9ba3680f3d50526a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9856ad2a8dd1b673ec2cfa9ee0a1eaff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184c6736108865aa9ba3680f3d50526a.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/184c6736108865aa9ba3680f3d50526a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/543a1701b0b6ab23d9a8690453717132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0f33f28247234029ae7589666c3f57b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
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解答题-问答题
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较难
(0.4)
解题方法
【推荐2】如图,数轴
的交点为
,夹角为
,与
轴、
轴正向同向的单位向量分别是
.由平面向量基本定理,对于平面内的任一向量
,存在唯一的有序实数对
,使得
,我们把
叫做点
在斜坐标系
中的坐标(以下各点的坐标都指在斜坐标系
中的坐标).
![](https://img.xkw.com/dksih/QBM/2021/4/19/2703265010499584/2706632514879488/STEM/ef3b9023-460b-4907-99f7-6c061655fe54.png?resizew=163)
(1)若
,
为单位向量,且
与
的夹角为
,求点
的坐标;
(2)若
,点
的坐标为
,求向量
与
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/111939547e581e8bf029a241b9e9cb05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b257fe21a91d22e853b1642c9d44647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://img.xkw.com/dksih/QBM/2021/4/19/2703265010499584/2706632514879488/STEM/ef3b9023-460b-4907-99f7-6c061655fe54.png?resizew=163)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b12fe9a4054ffbacca1b995751969a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c0927afc571a7c966c98192040979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c42206793edde00d2d43cd07adf78366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38620d68461307e424923b903ab518f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cec64476aaca08de0808afda3618109c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
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解答题-问答题
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较难
(0.4)
名校
解题方法
【推荐1】已知向量
,
.
(1)当
,
时,有
,求实数
的值;
(2)对于任意的实数
和任意的
,均有
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64f2b45d3a748f599fa82bfc93c6ef19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17dfbb2ca4618dbe985600a1e00e40be.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99c6875d552e9fff3c7d655f3a59b166.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89e063dc0b3b37e2ade6e3254bfa60a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d75de364157de37e496c2dd202682b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)对于任意的实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45607452209f65ed5269ef4da0907bb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad51d17e5d771c46ad2a6e6c478a94b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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【推荐2】已知:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fade53eab1e4ee2ddc13cbed312a0a1f.png)
(1)设
,求数列
的通项公式;
(2)在(1)的条件下,设数列
的通项公式为
,且
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
成等差数列,求m的值;
(3)在(1)的条件下,数列
,其中设
,是否存在
,对于任意
满足
?若存在,求出
;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fade53eab1e4ee2ddc13cbed312a0a1f.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa336f119050cbd6a42092f204b36447.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)在(1)的条件下,设数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/034ba25825c13725931c483aa47c9363.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e411143008ab1e453fe53dcc0aadcc85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b715e7842b95f654f16056a7c7f2abe9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13423c094861baf4b759b7f3d8c3c226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f64696f60c533ad95dc7890eb902741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc4166a931e94d58c69dea259e610275.png)
(3)在(1)的条件下,数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef6d44448092ebdb9e4a49d866a749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c733ce52923a39ddccda79ad4695e415.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/646dae47fe49e60090ccbf2d7180c1b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bf75f247f1af0a98e6ea44cf834b77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d7e9f86738335a22298559db41037a4.png)
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