名校
1 . 已知向量
,
,且
,则x的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eceddf10c35b43086f272079462aa51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3333b2dab42b2115812837411bdec3ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/460e5ba67828c57daf2edb497fb52e56.png)
A.-2 | B.2 | C.-8 | D.8 |
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2 . 已知平面向量
与
共线,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd989ddfbed4a6aa18ea57734522153.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a93944d382b73bb691719b868fd69a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f47f03ca8c235959f5dba54c6c83e7df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfd989ddfbed4a6aa18ea57734522153.png)
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解题方法
3 . 已知点
,若向量
和向量
同向,
,则点
的坐标为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8796f6d3e7a0e3771f83df47e99a970d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1ef4988b025cdf296ea81d7ef05f404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17178285fc30b77c846391467d3b0348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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4 . 已知
,
,
,且
,
与
相交于点P.
(1)求点C和点P的坐标;
(2)求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c95963e8e4dcc511f0d86b1853ddcdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af0acc212c5c94602deb68c86c33369f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
(1)求点C和点P的坐标;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a10f2c4a2a9c9cb4047f9f27cff1d7a.png)
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解题方法
5 . 设
,
是不共线的两个向量.
(1)若
,
,
,求证:A,B,D三点共线;
(2)若
与
共线,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c08ebbac3d6784d6d3565192f36f91a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e5f8509784fc0cc4134e41f8dcc0a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1af26762e8309eb14f2bcab0954f7165.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52395f0262abbf2a4b1a823b4b65caae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a126bb16b6ab8644a8e8d33f6909224.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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解题方法
6 . 已知向量
,
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/265ce956493513dc90ee46ec2218b72a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d8c466ff442f33b5d756e1723e2ccf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668f0254cf71230731ceb71bfc0e07a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
A.![]() | B.![]() | C.2 | D.![]() |
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解题方法
7 . ①
;②
;③向量
与
平行,在这三个条件中任选一个,补充在下面题干中,然后解答问题.
已知
内角A,B,C的对边分别为a,b,c,且满足______.(注:如果选择多个条件分别解答,按第一个解答计分)
(1)求角
;
(2)若
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bb275bed911a7dd2ac07726ea5b21a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4ec73f650839722a3dfd7e423ff1668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c70abdc05999ce71182564ca3c7c05d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab40cf4771794a8d3db1430a6936d3d6.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)求角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcb5bac75f36bb1dc5c8190d4dbe681d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
8 . 已知向量
.
(1)求
;
(2)求向量
的夹角
的余弦值;
(3)若
与
平行,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f382937f75a9c0bedba670ad9524e45.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb74499b8965b3f6c9acfbbb168df438.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e08d0ffb3a2147fb1ba5145471082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd8bbf47b69bbd7a6263b041290d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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9 . 已知向量
,
.
(1)若
,求
;
(2)若
,函数
;
(ⅰ)求
的值域.
(ⅱ)当
取最小值时,求与
垂直的单位向量
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01cf8a6998a3a4153321b6e75e1d45ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/067ed5f278f0175db62ba3fb642357c2.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66d76ee2e81f447f84a3e0b39c0388ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c679119740af166f73eee7d2f9702108.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/905dd10639c9fef5ef8d66a124756140.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7aa1233d7a93113281594c41f25c7db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b1034456462f4deca6a2ecbde758021.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(ⅱ)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
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解题方法
10 . 已知向量
,
.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______ ;若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355314f379eab30b26be60b334a2b9aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bb6e06a9deea9f51755b27320b44c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd79264e130de60a100b001b5d45585c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bf21fef3026cfe445a855c94cab5c84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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