已知平面向量
,且
,
,且
与
的夹角为
.
(1)求
;
(2)若
与
垂直,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03a5d2defc92b9cca77d4cb7ffd00652.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b9620b76a31e8cfef0cd6a2bdb10ffa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e3d33a8f66715e36bd0677ddc06313.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/2d88591679796c52024d11c4de641bdb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eebc03129bad1dfc7d85ee62145cc7b.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8a16a2ba41159e45b24e96d8576d21.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d3eab4818ba4b526c433351e1a4bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
更新时间:2021-08-01 07:39:47
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【推荐1】已知
,
与
的夹角为
,设
.
(1)求
的值;
(2)若
与
的夹角是锐角,求实数t的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da39efdb736a8cca9e8255db1209e939.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/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99b4424387029e52affe63eb9265e17.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355fb84afd357e2b8f310dfcc1075aa6.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560ee2894ba8c5cee6633430cc8b3b41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f1a8e551cba7ec9f451749f60e628d.png)
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解题方法
【推荐2】已知
,
,向量
,
的夹角为60°,
,
,则当m为何值时,
与
垂直?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5943afb8ca75e69aa03dee57f9ae0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e3d33a8f66715e36bd0677ddc06313.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/c316d5fee573243bf9c9dd28a5ae215e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8f3a19519614832e9c5ceb1dfbe49d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec655f610928ca21831e26645a21e99c.png)
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【推荐3】已知向量
满足
.
(1)求
的值;
(2)求向量
与
的夹角
的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ee1323e38f79942705b1a297c00a0b8.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8e7d56e6c193b4ca6c896e6ad90860.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffa3e1ce447d158f6084a66841307a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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【推荐1】已知向量
,
满足
,且
.
(1)求向量
,
的夹角;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93941bed16180b784886058ad2dd43dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3aa5275170d0cdb6f28e61371171d74c.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d2840834a09f5c5da5381d9e4b6f434.png)
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【推荐3】已知
,
,
与
的夹角为
,计算下列各式:
(1)
;
(2)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3ae7b0214b4817a69014bf74bd10a17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e405db6c09d6ab5739cabbb63cd3b3bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e7577c538c53da9db6db659a00060d4.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781c445660625e3304602c62c183c9a0.png)
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解题方法
【推荐1】已知向量
,
,
与
的夹角为
.
(1)求
及
;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5943afb8ca75e69aa03dee57f9ae0c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e3d33a8f66715e36bd0677ddc06313.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/2d88591679796c52024d11c4de641bdb.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63740ffa63265af7c4a42a13c6fa6279.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f11ac1bd265894c8057f665c203051e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc7c3657a814f48516bb9b3a6e61f745.png)
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【推荐2】已知
,
为一组单位基向量,且向量
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ad70ed868814e5057b6a4123465a9f.png)
(1)若
,
(其中
,
是方向分别与x,y轴正方向相同的单位向量),
,求x的值;
(2)若
(其中的e为无理数,
…),
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b04618e5b2db68f2de6ba68972c505c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69613c3bd6e8ab69a6bafc8de92af70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ad70ed868814e5057b6a4123465a9f.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab03ad7afacbcbec765ce4fc5ec511cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9d93888ae28aa1262fbd6ea40f1aff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d753a0a27ec4302346bcee918ebd3e50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2079be0b9d0919862ca5bc8ea565f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/069da5c624837df29947b7b8bf722097.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1880e3bb442d478b6dca1ab56eb054ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62ec4e8e4b8863af9774bcd739a73ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e4e3c71ea833a4aefb79542a2e0fbbc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8d40e257f9c446b8e30fa841b74bbd.png)
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【推荐3】已知向量
与
的夹角
,且
,
,求
与
的夹角的余弦值.
![](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/fca81a3bdf849b4c9ebb73854d54b92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9936a46cc891744d4600f76bb92b694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da08da2af81a46e41d2e5eba47acf20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73b91254db5ff748150f449c5cdd256c.png)
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解题方法
【推荐1】设
为实数,已知
,
,
与
的夹角为45°,且
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f18996bd00253c3ad9f91780103affb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/939955fcd19578dc8f37415c60b187ab.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/f66b668c89050f22f74d8ec332582edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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【推荐2】已知
中
是直角,
,点
是
的中点,
为
上一点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/504981b4-d16b-4f9a-9ed8-e1ac03cf0de0.png?resizew=112)
(1)设
,
,请用
,
来表示
,
.
(2)求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d89ba4036a5d18ec4abed44d7fd8e89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b1bd1adfe4cc6566218f19970c2fd3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd79c93167255ec796a0f4b4678516d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/27/504981b4-d16b-4f9a-9ed8-e1ac03cf0de0.png?resizew=112)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c4bbde083fab7885ebe1b796785a502.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/391fa1d1e2294caee6845f67e34d861a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a92e6eba8dab638fd66831cd3a0b6d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/427fa45527d0ce469bfd060bf6f991f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/228f4ddbb8959f904d71259be7c6ab36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72d7692fcc50f53076996644c7c3f27a.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd5c41c921836b50f8e18abfdc5df3.png)
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【推荐3】已知
,
,
.
(1)求
;
(2)求
与
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd18461fd9d77e6fa46a654f0ab540f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082c6926889f84f438ea35f70bf05f02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651ea21709173040f2fb60e343422891.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b0fe4d834e8eaca89ceaf9c64cdabd9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f1c1dd6b13d92f2cc2eef097e14c07c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
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