解题方法
1 . 对任意两个非零向量
,定义
.若非零向量
,满足
,向量
与
的夹角是锐角,且
是整数,则
的取值范围是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662917aedec92809a13618093c8e0c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63c7ac4b4b9924ef29792fa6ac198f06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26739971f3cae6d4790870c344b5cf89.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/b35bee611ba4204db25848d5925c618d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4db35dbee504e3e66bfd03c24e4b7322.png)
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2 . 已知某扇形的半径为
,周长为
,则该扇形的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/354ec8391bdd39377804ee4dab1d8f1c.png)
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3 . 如图,为了测量某建筑物的高度OP,测量小组选取与该建筑物底部
在同一水平面内的两个测量基点
与
.现测得
米,
20米,在测量基点
测得建筑物顶点
的仰角为
,则该建筑物的高度OP为____________ 米.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e720e101184647f20c062a492e5b67af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a836d2dfc31d2bfc949bac8403cf2a4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
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7日内更新
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3卷引用:河南省驻马店市经济开发区2023-2024学年高一下学期第三次月考数学试题
4 . 如图,已知山体
与山体
的底部在同一水平面上,且两个山体的高线
与
均与水平面垂直,
,在山体
的最高点
处测得山顶
的仰角为
,测得山底A的俯角为
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
______ m.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243ed8748dea92fa90d5789d1ab69435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79a97bb4dcfab4ec7539bc783d563c49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c978d92edf0c4c1ef8620c17df75d35e.png)
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2024-06-16更新
|
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2卷引用:河南省驻马店市部分学校2023-2024学年高一下学期5月青桐鸣联考数学试题(北师大版)
名校
解题方法
5 . 若向量
与单位向量
的方向相同,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c56bd77e10fa9f8952c0660c1fce5d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e4090e8ad8d7d99056c4a143a5eb4fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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2024-06-16更新
|
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2卷引用:河南省驻马店市部分学校2023-2024学年高一下学期5月青桐鸣联考数学试题(北师大版)
6 . 已知
为钝角,且
,角
,
,
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2896049a682f1bdbee0886eae1f2b9.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2201ec2556638a0a9401137b8c070d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b6612254a68353e3f6879f7d72ffd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df2896049a682f1bdbee0886eae1f2b9.png)
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7 . “天封塔”位于宁波市海曙区大沙泥街西端与解放南路交汇处,是宁波重要地标之一,为中国江南特有的仿宋阁楼式砖木结构塔,具有宋塔玲珑精巧、古朴庄重的特点,也是古代明州港江海通航的水运航标.某同学为测量天封塔的高度
,选取了与塔底
在同一水平面内的两个测量基点
与
,现测得
,
,
,在点
测得塔顶
的仰角为
,则塔高![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
_________
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc344dd373075c8ae2f1433ae499afd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07ed8cd374bffba6ce3982fd2f21e277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654c72112fbd42d180877a2dadbc9774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c26a46e7879436d532af3f4b6e258a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e15e00f40396e914d1d9955bd7785f1f.png)
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|
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名校
解题方法
8 . 如图,圆
为
的外接圆,
,
,
为边
的中点,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d006bdb8336b4bcc5ba7dc2fd81f3614.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1682d306c38087d9e6f7efb9cec596a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d006bdb8336b4bcc5ba7dc2fd81f3614.png)
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|
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4卷引用:河南省驻马店市新蔡县第一高级中学2023-2024学年高一下学期5月月考数学试题
河南省驻马店市新蔡县第一高级中学2023-2024学年高一下学期5月月考数学试题福建省福州市第十五中学等五校2023-2024学年高一下学期期中联考数学试题山东省菏泽市第一中学八一路校区2023-2024学年高一下学期第三次月考数学试题(已下线)核心考点2 平面向量的数量积 B提升卷 (高一期末考试必考的10大核心考点)
名校
9 . 中国扇文化有着深厚的文化底蕴,是民族文化的一个组成部分,其中扇面画有着悠久的历史.某扇面画可看成一个扇环,其示意图如图所示.若
,且该扇环的周长为
,则该扇环的面积为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a5ccec0e8c65a21a65a5149ef1c01d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a00c640bc632356806c12ee45f50be09.png)
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2024-05-08更新
|
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|
3卷引用:河南省驻马店市新蔡县第一高级中学2023-2024学年高一下学期5月月考数学试题
河南省驻马店市新蔡县第一高级中学2023-2024学年高一下学期5月月考数学试题辽宁省本溪市县级重点高中协作体2023-2024学年高一下学期期中考试数学试卷(已下线)专题07 一轮复习三角函数(1)--高二期末考点大串讲(人教A版2019)
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10 . 已知
为平面向量,且
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17413ca9b1286ed354edc6c20ba09a2b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6316d995f00623f05fc3d56a6cbe5f00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407538138dd68ab917925c2063cc98e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71d948505a1b80b5d814137310025eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17413ca9b1286ed354edc6c20ba09a2b.png)
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