1 . 已知向量
,向量
是与向量
夹角为
的单位向量.
(1)求向量
;
(2)若向量
与向量
共线,且
与
的夹角为钝角,求实数x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b0d67bda3986d22b6cb82070864b4fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50e897700e0b9e8e31e677b4d241dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e45f0fae461881d999e14a3de613e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0bf9e42f4ba6772a859da00df960714.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50e897700e0b9e8e31e677b4d241dc1.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50e897700e0b9e8e31e677b4d241dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e4beab0ea942209772744e0438d391d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50e897700e0b9e8e31e677b4d241dc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24ce3015cea94778d0c740d3593e5d4e.png)
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2 . 已知向量
与
,
与
夹角为钝角,则
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4f40def777e1d7c7ced828899ed593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b5f2fd9f3f3c3be001ea38411440644.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
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3 . 如图,在正三棱柱
中,
,点
,
分别为
,
中点,求:
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/c2045a5b-13d1-464c-b797-2ab60176bd54.png?resizew=124)
(1)异面直线
与
所成角大小;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92105835f8075cb75dff244e908370b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/c2045a5b-13d1-464c-b797-2ab60176bd54.png?resizew=124)
(1)异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbc96c20ebba91031a1c54037fe651c.png)
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4 . 已知
,且
与
的夹角为钝角,则
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4601a02fd28c12c6d4abbb937cca878.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知两点M(-1,0),N(1,0),且点P(x,y)使
,
,
成公差小于零的等差数列.
(1)求x与y满足的关系式,并写出x的取值范围;
(2)记
为
,
的夹角,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6eb7c8a01467044f11abe5fc7081995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1f4ea7498731e5af223a75a5ab7f32c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eee62ddc19a7f5eb488936c4d6c83978.png)
(1)求x与y满足的关系式,并写出x的取值范围;
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f5ad849321c004834b89b6d26594e32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc37a21e51692ea9acb99ff0a25ae280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43660b1543b3a2b46185f7629d28a963.png)
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解题方法
6 . 在长方形
中,
,
.M,N分别是线段
,
的中点,P是长方形
(含边界)内一点.
(1)求
的值;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09d27bd71d79cb19eb554175e4ef0867.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4ae4881d290a010988db3eec009ab4.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/442e34f9ebda5c3ac4a106d9ad371e6b.png)
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7 . 在三角形
中,
,
,若
对任意的
恒成立,则角
的取值范围为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f83b02dc7659d7fdad5771da6996d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa955ce6097b1ee327bd51000693b6e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abb9b2ab27e9ed2826024b85bfee8797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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8 . 在一个平面内,一质点
受三个力
、
、
的作用保持平衡(即
、
、
的和为零向量),其中
与
的夹角为
,
与
的夹角为
.
![](https://img.xkw.com/dksih/QBM/2019/10/23/2317988587274240/2318182808379392/STEM/36e1c720b887490193ee94dca77427a8.png?resizew=245)
(1)若
,
,
,求力
、
的大小;
(2)若
,求
与
.(用反三角函数表示)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0985912f741bd0934b10c52452fc9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c48b15e8d588d0ac4b5f8e23c768f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d4b28d9326c4adfe9e4c783dba6be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0985912f741bd0934b10c52452fc9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c48b15e8d588d0ac4b5f8e23c768f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d4b28d9326c4adfe9e4c783dba6be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d4b28d9326c4adfe9e4c783dba6be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c48b15e8d588d0ac4b5f8e23c768f4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24d4b28d9326c4adfe9e4c783dba6be1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0985912f741bd0934b10c52452fc9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://img.xkw.com/dksih/QBM/2019/10/23/2317988587274240/2318182808379392/STEM/36e1c720b887490193ee94dca77427a8.png?resizew=245)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0174ecb3effe04d6137463dcad183c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/babb6061825778a790b2fde1d4267abd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169f306435e6b77fd17d906807f0ba39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0985912f741bd0934b10c52452fc9a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c48b15e8d588d0ac4b5f8e23c768f4a.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/302bb56306d04e9d06667c1a8920455a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
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9 . 已知点O为
的外心,角A,B,C的对边分别为a,b,c.若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0252977d38df16845da8b27885aed987.png)
_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0969251615dbdc6142d58e4bbf8115ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0252977d38df16845da8b27885aed987.png)
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2019-10-16更新
|
315次组卷
|
3卷引用:高中数学175
名校
10 . 设
,若
与
的夹角为钝角,则
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2ae22a5366eb4ccd2977b706072d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf611ba33980c2b94067406cc3804a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c76d58f076f37bfb0a7200ecb7d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
您最近一年使用:0次
2019-12-11更新
|
239次组卷
|
3卷引用:上海市位育中学2018-2019学年高二上学期10月月考数学试题
上海市位育中学2018-2019学年高二上学期10月月考数学试题上海市位育中学2020-2021学年高二上学期10月月考数学试题(已下线)第8章 平面向量【真题训练】-2020-2021学年新教材高一数学下册单元复习一遍过(沪教版2020必修第二册)