23-24高一下·贵州贵阳·期末
1 . 已知向量
,
.
(1)若
,且
,求向量
在向量
上的投影向量的坐标;
(2)若向量
,且
,求向量
,
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1462c1fed1d82541fe6e8cfeab430e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d49a216512c1d79f21f3e7d4243894a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e51ee815e7260e25b5709b85ea895748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f0e9c04402a0ffdaa25c3e3c82c7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adcad563f5a6828760ffb8f3aedfd318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcdc1bf6047bdfa7aea068dd842db407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
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23-24高一下·贵州贵阳·期末
解题方法
2 . 人脸识别就是利用计算机检测样本之间的相似度,余弦距离是检测相似度的常用方法.假设二维空间中有两个点
,
,O为坐标原点,定义余弦相似度为
,余弦距离为
.已知
,
,若P,Q的余弦距离为
.则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb682915a0328ea22592dfaefb12d6f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ca8adf58d1daaadc443166ed7f828e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/926778fe15991308849cdba1822595a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451fc6e4248b63e70595f23842f06c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca91fb61603b4bfa6dc993a34e1736d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b33a6d043c8bde2a70bdf22623fa3c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 如图,在正方体
中,
在线段
上,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1ba61f50c7429166adadf8fa21c3627.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e539f26ed5e0b20ff7220559324869a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916b3d8066e0080eaf76ddf07651a076.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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(已下线)贵州省贵阳市南明区部分学校2023-2024学年高一下学期6月联考数学试题湖南省郴州市第一中学等校2023-2024学年高一下学期5月联考数学试题重庆市璧山来凤中学等九校联考2023-2024学年高一下学期5月月考数学试题(已下线)专题10 立体几何中最值问题【练】(高一期末压轴专项)
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解题方法
4 . 已知向量
,
,
.
(1)若
,求
值;
(2)若向量
在
方向上的投影向量为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81f4dcf415977dea53f52a85b6b82136.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b1305dff4fc89f3e8bc75fa7c258de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab00543b1f4647a7249fe5a4507e1ec1.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b610fe3872cd8c1009b6a3e0111bacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed492f7b29166ba5c1f0023b05a439c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cef9c6d3fc0c7d3ec11c782fd106511.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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解题方法
5 . 已知向量
,
,且
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61df6db5f13202396a800df639732c9b.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e139e7cec9ef14acedae556ebcd9fc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0601da78869330b870d420dbebc674.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2558ead24d56fb372fef95c10fddd3fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61df6db5f13202396a800df639732c9b.png)
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6 . 如图,在正三棱柱
中,
为
的中点.
平面
.
(2)求异面直线
与
所成角的余弦值.
(3)在
上是否存在点
,使得平面
平面
?若存在,求出
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5362fa29dbedcdc84cda3dc5f8165c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0186d11008c7d66c85ed0d8d2e568908.png)
(2)求异面直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d8772aa893a9c1d40f714cb25701701.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93ecad355286188fd317939fa50f9555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39282bdf319f30d7bc261e2e3ab3b1e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea848cd2aa3a464618020475097949fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bdc02a625fbfdd1b50c1796c1e33e95.png)
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(已下线)贵州省贵阳市南明区部分学校2023-2024学年高一下学期6月联考数学试题湖南省郴州市第一中学等校2023-2024学年高一下学期5月联考数学试题广东省广州市真光中学2023-2023学年高一下学期月考数学试题
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7 . 如果对于函数
的定义域内任意的
,都有
成立,那么就称函数
是定义域上的“平缓函数”.
(1)判断函数
是否是“平缓函数”;
(2)若函数
是闭区间
上的“平缓函数”,且
,证明:对于任意的
,都有
成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c2f1ca03ade14de6711c85de8fc5df0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)判断函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ea19565e4feac073e898ab188fc3f5.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aeb3ca8cbc4facb2467b1a618f33794.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83a6c0fddb9074dfc96be03b4aa24d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e9387190a323961884c302798c9e4e.png)
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解题方法
8 .
的内角
的对边分别为
,满足
.
(1)求
;
(2)
的角平分线与
交于点
,求
的最小值.
![](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/008a9e8912d20e215500cd5a2a2e3a73.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d39b8d91afc34e4a9b0fdbb6bafb9087.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e14d71667c64ab37596ff76207c7a82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451be539a00c5a0fa9e00fc9bf4c39fd.png)
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9 . 如图,在四棱锥
中,
,
平面
分别为
的中点,
.
平面
;
(2)求二面角
的大小.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72f089b54ee14e369cf48b528477a64e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58bf40f6235d0231481c2598e2ba977b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb46aaae98bce8e66848e09c2c1cdbd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9801cabc43c024b9c5fac34b7db5d69b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d077f6da8b2c00b152d4679aa2ed7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03428a8f91a5674cb8f54766c165f7e.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5617a404c5a3356753136e5a6b6d51e5.png)
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10 . 设两个向量
满足
.
(1)若
,求
与
的夹角
;
(2)若
的夹角为(1)中的
,向量
与
的夹角为锐角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b904ee9b19e35b3fef137fb02a654f8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d062b28cf7f9dbbba15c2d7769b98cb.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/c24095e409b025db711f14be783a406c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12dfa2b2e9488107d07fdac71f433774.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6d7ba9c5074d45752fb01ade0f441d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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