解题方法
1 . 设M为
内一点,且
,则
与
的面积之比为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6a216ebd7cb82c1a9706c325df53371.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cad3e2b2689dfe97ec82d473ab6cf469.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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2 . 已知
中,角
所对的边分别为
,
,
,
,若
,则
的最小值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c95d62b9a1fc994c972781c7013fedba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb1b5305cb9b5a90c4f13bceaaee4fc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68918379531894442f55c7257549ea33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd5b9bbd3d22bd2cef53dd4b9691257.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09c4807435a3e91de8aba99db62e23bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e0987a20a5648765bce6ae78a693106.png)
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解题方法
3 . 在平行四边形ABCD中,若
,
,则平行四边形ABCD的面积为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42083f00cd68320e4e0275400c139551.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/499fd1c359cd78bf067326e4b940acee.png)
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2024高一下·全国·专题练习
4 . 如图,直径
的半圆,
为圆心,点
在半圆弧上,
,线段
上有动点
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c161375e4e6f61f1cbef8083c02e975.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d493b2b9d5e5132eee3f74aa8fabfbab.png)
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2024高三·全国·专题练习
解题方法
5 . 四边形
中,M是
上的点,
,
,若N是线段
上的动点,
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff9554b78070407bfc62f15b78a4fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43c5cc60056f89af454378cd8bd11c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/340f84b11637ee42eaeeec250d0f0c29.png)
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解题方法
6 . 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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2024-05-08更新
|
686次组卷
|
4卷引用: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
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河南省驻马店市新蔡县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
解题方法
7 . 在
中,
,
,
的平分线交
于点
.若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/806d90355769e53ce347d24bf764506d.png)
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5407daad0b0a876e5d9d5f5191642fad.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e3262fc038bbec5e7c8cc47df08bef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d3c9ce32b721995f355eea411340e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/806d90355769e53ce347d24bf764506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8704be017325107e21d541e816690b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5407daad0b0a876e5d9d5f5191642fad.png)
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8 .
与
是两个单位向量,
,则当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
______ 时,
取得最小值.
![](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/4ca6b59bdd54ca0cc3632409dfb39dd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d882913c702822a27f07c06ea005a1f.png)
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9 . 如图所示,平面四边形
由等腰
与等边
拼接而成,其中
,
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccef95e79dfa4d8801824f5874cfda08.png)
_________ ;若
,则当
取得最小值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab2a2834d80ff574e79eae8ca8d4e94f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/661ff55b5ebbadfb600989af3cfce2fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2aabb3232e9ffabad9def25515cbdc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e735a28578ba191da6d4f3b0f8e8729.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07160f14b3b453bebb64cb2bf96dc85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccef95e79dfa4d8801824f5874cfda08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dfbedbad650c4723ff6d95fef4fc47c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/992907998c85cf872f6e66df0b0c1030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
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解题方法
10 . 在四边形
中,
,点
是四边形
所在平面上一点,满足
.设
分别为四边形
与
的面积,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5c145e588834d756ea8a81504abce4.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a166eb8b7caa853b8b28bf86e70fe24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0b7eaf847d85bcf033f2b17ccb5158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b056a90a2751f04ba5fff3dc5c1d0674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5c145e588834d756ea8a81504abce4.png)
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2024-04-30更新
|
276次组卷
|
4卷引用:山西省长治市上党区第一中学等校2023-2024学年高一下学期4月期中联考数学试题