已知向量
、
、
在同一平面上,且
.
(1)若
,且
,求向量
的坐标;
(2)若
,且
与
垂直,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddac50ca9d89729c6ac4a5d687bd3b0e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b580b1e474eb43d7e7e2634ece223036.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ffda24d6f7d8823d65c7ee67f2996d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b9c10afcf033262946f4f874455bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/496590f060e41cbaca42b9eaca3cc6f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697e82d288df5ac7656340301e636646.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
更新时间:2021-08-13 15:41:43
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解题方法
【推荐2】已知向量
,
,
.
(Ⅰ)求
;
(Ⅱ)若向量
是单位向量,且
与
共线,求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6569e50f43b3d8645652ecc13b62066e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fda31d7cbc3ee5de962806c251afc2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec1cc86b7ff004a6ab4f88b7af2d58da.png)
(Ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(Ⅱ)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/441b83f50b3a9452693467b342b7ab04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec42c3751963b1ab1f0cf16df8701bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
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【推荐1】已知向量
,
,
是同平面内的三个向量,其中
.
(1)若
,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
,求向量
的坐标;
(2)若
是单位向量,
,求
与
的夹角
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc038d02f8c463d4102ac1d730408e6a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ed0703d32bda90a21d7c3d329e0b14f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895d6f710d5f67e1d4c7408d50d77281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba82d5aece4691ea007fa1682f61654.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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【推荐2】已知在平面直角坐标系中,
为坐标原点,定义非零向量
的“相伴函数”为
,向量
称为函数
的“相伴向量”;记平面内所有向量的“相伴函数”构成的集合为
.
(1)已知
,
,若函数
为集合
中的元素,求其“相伴向量”的模的取值范围;
(2)已知点
满足条件:
,
;若向量
的“相伴函数”
在
处取得最大值,当
在区间
变化时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10340e091d449def212223acd93a4269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/014596e97b52f22597ff68cc5b0616a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb66f4db41478c23128adc14f2796556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ab65cb6a94429813529ad6bd1f45476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2d6bb01f1044358cc5fee441bc62489.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7d4d2a7191b6c58469a9c2b3856bf85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11abb76da45ffa52b47c3a6b9a03ac7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f82446db626bc1ff915cd0c8b12cee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63e0e24323fe73e5d9fc6136219306da.png)
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【推荐3】已知在平面直角坐标系
,向量
.
(1)求与
垂直的单位向量
的坐标;
(2)若向量
,且
与
的夹角为钝角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a08ed47d6563ffa369eec7374cccffd.png)
(1)求与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc64abe49847ade9b78678ba1f8e0e2.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65bd2bc4e1a28a6ef13487447ea4747f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0be59eb3dc3d5ea7be8cd4add057470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b83c5803cc8c05849028a57c4bd4ee72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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【推荐1】如图所示,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf16b3b155aa924b607ba11048745e10.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/cf96944f-b817-4f3e-8df3-14856b93622b.png?resizew=155)
(1)若
,求x与y的关系式.
(2)在(1)的条件下,若
,求x,y的值及四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2c4885e81837c185da076dbc7dcd70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a1d27a95a65d5f5c0b0bc2b1471d855.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf16b3b155aa924b607ba11048745e10.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/29/cf96944f-b817-4f3e-8df3-14856b93622b.png?resizew=155)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16335a23fce896ca6b5a25bcae9272b5.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc9448c4e9a71c0ec8a1de4904b7bd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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解题方法
【推荐2】已知向量
,
,
,其中
是坐标原点.
(1)若
为直角三角形,且
为直角,求实数
的值;
(2)若向量
满足
且
,求
的坐标;
(3)若点
能构成三角形,求实数
应满足的条件.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7b4db13da652aee3db488683c13fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c38a0d35007dced5215cdede5c7f250.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b504a592d6f21133322d0428314de1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febc9a89d0d1c97b88c0f4acd32b4e67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10c8b60c45bdd5a49b5c130e755d9e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a195f3689d890951b74554c4e4b7063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c739db1fc94f894343497a60cd12b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10c8b60c45bdd5a49b5c130e755d9e8.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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【推荐3】已知向量
.
(1)求
的夹角;
(2)求
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/038f4b7a58e12a480c332467ccd2a754.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
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