解题方法
1 . 已知平面向量
,
,且
,
,向量
满足
,则
取最小值时,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9a5451e35042092a0cdc5971a4d55e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e37157acb52896b1d3d067adc7d381b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d366d8fbb7258ee051f49977441e14a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59d3e5619718e1bb2592caf48bcc2718.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5b0a4509691f41732a190fceef0175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5085e3cdef9ea6c564e079f745d6fdb.png)
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2 . 数学中有很多相似的问题,
材料一:十七世纪法国数学家,被誉为业余数学家之王的皮埃尔·德·费马提出了一个著名的几何问题:“已知一个三角形,求作一点,使其与这个三角形的三个顶点的距离之和最小”,他的答案是:“当三角形的三个内角均小于
时,所求的点为三角形的正等角中心,即该点与三角形的三个顶点的连线两两成角
,当三角形有一内角大于或等于
时,所求点为三角形最大内角的顶点”,在费马问题中所求的点称为费马点.
材料二:布洛卡点,也叫“勃罗卡点”,定义为:已知
内一点
满足
,则称
为
的布洛卡点,
为
的布洛卡角,1875年,三角形的这一特殊点,被一个数学爱好者——法国军官布洛卡重新发现,并用他的名字命名.
已知
,
,
分别是
的内角
,
,
的对边,且
.
(1)求
;
(2)若
为
的费马点,且
,求
的值;
(3)若
为锐角三角形,
为
的布洛卡点,
为
的布洛卡角,证明:
.
材料一:十七世纪法国数学家,被誉为业余数学家之王的皮埃尔·德·费马提出了一个著名的几何问题:“已知一个三角形,求作一点,使其与这个三角形的三个顶点的距离之和最小”,他的答案是:“当三角形的三个内角均小于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e4979100d4078609e253e2f99eed0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e4979100d4078609e253e2f99eed0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e4979100d4078609e253e2f99eed0b.png)
材料二:布洛卡点,也叫“勃罗卡点”,定义为:已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c25d734ea37934683320c146c2c67a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/481b91aa00df0bf153f717d87d1b12f7.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54728823efd2745d64ae9921f8807917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1424f6ac5e01f56e2d486c68a5be1a0.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e428e7a09732be85c1224e9c8f6a71c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26f61d98c51b9f0344cf7b4562680f45.png)
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3 . 已知三棱锥
的四个顶点均在同一球面上,
,
,且三棱锥
体积的最大值为
,则该球的表面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e45b0e1c3f6f5bc4cc81290bf263d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d70dc2c20619a4fc12a0cfda59af5b69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e5db1d2fd912f77923e4c120a7dc19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 函数
的图象如图所示,图中阴影部分的面积为
,则函数
的解析式为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/473c9fea4cdded9be6f12958770c0cf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997b5842f3d4eae1989debee9ae41b9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0afb80007983e5b99dcdeebf87d18ff4.png)
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7日内更新
|
83次组卷
|
2卷引用:辽宁省大连市滨城高中联盟2023-2024学年高一下学期5月期中考试数学试题
5 . 如图,在直角
中,
分别为边
上的一点,
,设
.
时,求
的长;
(2)当
时,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c578a8282d443e6ac78f6724b37cc32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/374fe9986ebbc986fc422e514ab93a51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6022c708eae22d66c3a75b22f78f2206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226eb5bc243dc12d2b334401b37fb51e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65844ad7d410463e70288b6d20a5f4c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5447a70b9197de4d2814c227a33b42fc.png)
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名校
解题方法
6 . 已知
,
分别为该三角形的垂心、外心,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91219670f597461ea7c6b7f259ff039a.png)
A.若![]() ![]() ![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若![]() ![]() |
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2024-06-16更新
|
480次组卷
|
2卷引用:辽宁省大连育明高级中学2023-2024学年高一下学期期中考试数学试卷
名校
解题方法
7 . 某工业园区有
、
、
共3个厂区,其中
,
,
,现计划在工业园区内选择
处建一仓库,若
,则
的最小值为( )
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd46f78d1641e1f10e38dc7864d6703b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cf1ebaf51acdd9c790c17053cffb7d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acdbac251ca6b76a166c1242e71df9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b3bfde4b7cbca10de7d63bb7b2cfd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-06-13更新
|
1047次组卷
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3卷引用:辽宁省大连市第十二中学2023-2024学年高一下学期6月份学情反馈数学试卷
辽宁省大连市第十二中学2023-2024学年高一下学期6月份学情反馈数学试卷广东省六校(北江中学、河源中学、清远一中、惠州中学、阳江中学、茂名中学)2023-2024学年高一下学期联合质量监测考试数学试题(已下线)专题02 平面向量的应用-《期末真题分类汇编》(人教A版2019必修第二册)
名校
解题方法
8 . 已知
,
均为锐角,
,则
取得最大值时,
的值为( )
![](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/dc394c19712cbbef1c781a6a8286dd59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cc9750c313ee972124cb62c4a6fb7ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e673f7e66c2a252da4c77c70d90c8cec.png)
A.![]() | B.![]() | C.2 | D.1 |
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2024-06-11更新
|
582次组卷
|
3卷引用:辽宁省大连育明高级中学2023-2024学年高一下学期期中考试数学试卷
名校
9 . 在
中,角
所对的边分别为
,
为平面内一点,下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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名校
10 . 已知函数
,则下列说法错误的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97b008969eee5d2990c094a88c829e18.png)
A.![]() ![]() | B.![]() ![]() ![]() |
C.当![]() ![]() | D.![]() |
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