名校
解题方法
1 . (1)已知
,
,点
在线段
的延长线上,且
,求点
的坐标;
(2)若
是夹角为
的两个单位向量,求:(i)
的值;(ii)函数
的最小值;
(3)请在以下三个结论中任选一个用向量方法 证明.
①余弦定理;②平行四边形的对角线的平方和等于其四边长的平方和;③三角形的三条中线交于一点.
注:如果选择多个结论分别解答,按第一个解答计分.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98b2cc0d2f6d3eee9a33db83e0c0830d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8a31b5335186eb1bea5c80cddcfd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e490ca1cc66be5a2f1677d243fe093db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8e8b95a61af300412fc65f846089028.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58054eff6c328eb401995a81c6e91a54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d65f84320b2cea4c64a8254bbceb250.png)
(3)请在以下三个结论中任选一个用
①余弦定理;②平行四边形的对角线的平方和等于其四边长的平方和;③三角形的三条中线交于一点.
注:如果选择多个结论分别解答,按第一个解答计分.
您最近一年使用:0次
2 . 定义
三边长分别为
,
,
,则称三元无序数组
为三角形数.记
为三角形数的全集,即
.
(1)证明:“
”是“
”的充分不必要条件;
(2)若锐角
内接于圆O,且
,设
.
①若
,求
;
②证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](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/10a57d1215099fab4a97db12b2fa8f14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c53315b1196d5a34560cc77995f817d.png)
(1)证明:“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c53315b1196d5a34560cc77995f817d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7b83cd3d2de78fbc430205d724b8edf.png)
(2)若锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a9c6bcfb1f63e1e57cccbcfb07e885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3641602ab775f0425debe0ec778c0ba2.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc6dfc6ee5b72469c51c6b5cc44ad72e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0839f7ef584b094ff45fdf01bb8f117e.png)
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90dfb13026887496470c48ed52e46fb0.png)
您最近一年使用:0次
名校
解题方法
3 . 已知
,角
、
、
的对边分别为
、
、
,
、
均在线段
上,
为中线,
为
的平分线.
,求证
;
(2)在(1)的条件下,若
,求
;
(3)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cbce11aa19b8bd2bf6ee5a834e005de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14342c5f52a0f5d34f58fc938bfe62a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe29c42302504e7fd8577dbc7d130ac7.png)
(2)在(1)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f3e693ef0f9f5ff9aec5bf7480ea18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1311f32edf13f8caee5edb03f24a7ba.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8021ba713186ce728699dadb321a612d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
您最近一年使用:0次
2024-04-12更新
|
513次组卷
|
3卷引用:重庆市长寿中学校2023-2024学年高一下学期学段考试一(4月)试题
4 . 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)
您最近一年使用:0次
2024高一下·上海·专题练习
解题方法
5 . 用
分别表示
的三个内角
所对边的边长,
表示
的外接圆半径.
(1)
,求
的长;
(2)在
中,若
是钝角,求证:
;
(3)给定三个正实数
,其中
,问
满足怎样的关系时,以
为边长,
为外接圆半径的
不存在,存在一个或存在两个(全等的三角形算作同一个)?在
存在的情况下,用
表示
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06fcf8777e54ba6078e0efe810a355b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194741f4d2ae7ee44cafca780361446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd0be39076f8a9425300e88e60ee9052.png)
(3)给定三个正实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2c659396f6a0f72e213185b1ab2e198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15bd315b801f71bc30b8d772098614.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aadb354aceba145fa22173f87a00488.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
您最近一年使用:0次
名校
解题方法
6 . 在
中,内角A,B,C的对边分别为a,b,c,BC,AC边上的两条中线AM,BN相交于点P.
,
,用
,
表示
;
(2)证明:
;
(3)若
,
,
,求∠MPN的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3adc4ed291596abf3bb93ae7a075d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cc03a3ba496faee748a8d63e5d4fa92.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/f7239b3f2d88c2e45e17e5de9ae1a332.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad18017b1c4f15f274f44bd4410a8b07.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/addb8e20db1fbb40f17dea52f951b907.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57fdd2a3642716fcf5100011eb3ec88.png)
您最近一年使用:0次
7日内更新
|
172次组卷
|
2卷引用:广东省深圳市光明区光明中学2023-2024学年高一下学期期中考试数学试题
名校
解题方法
7 . 在
中,角A,B,C的对边分别为a,b,c,其中
,已知S为
的面积且满足
.
(1)若
为锐角三角形,求
的取值范围;
(2)法国著名数学家柯西在数学领域有非常高的造诣.很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.若P是
内一点,过P作AB,BC,AC垂线,垂足分别为D,E,F,借助于三维分式型柯西不等式:
,
当且仅当
时等号成立.求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3efc64a6c2f8e31c8584cbbd5a2b3cb.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/413323ab92f73c1eabb235731bb5c399.png)
(2)法国著名数学家柯西在数学领域有非常高的造诣.很多数学的定理和公式都以他的名字来命名,如柯西不等式、柯西积分公式.其中柯西不等式在解决不等式证明的有关问题中有着广泛的应用.若P是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcbd8d6468c909aa229f527bca2581e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48a95e7d22d75a3a7a7c72df362f91fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5ba135022def1bcc1cddea66496706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69e37017b56a9d4d100413cf4bc16f4.png)
您最近一年使用:0次
名校
8 . 类比于平面三角形中的余弦定理,我们得到三维空间中的三面角余弦定理:如图1,由射线
、
、
构成的三面角
,
,
,
,二面角
的大小为
,则
.
中,平面
平面
,
,
,求
的余弦值;
(2)当
时,证明以上三面角余弦定理;
(3)如图3,斜三棱柱
中侧面
,
,
的面积分别为
,
,
,记二面角
,二面角
,二面角
的大小分别为
,
,
,试猜想正弦定理在三维空间中推广的结论,并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa26fadeee2becc192fa53d778445d52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac229a5e782559ffb0f271cbfc01c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef6ab2d197160f40b72fe0abb3fe527d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a438393ddfc7da1804baf4932442bb35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae6a7725d31fb74e974e2e45ba56805a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0671b4776e142e17a79af5b3f0378ef7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f70d708336d4f15e7fca0b26acb353b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73152c2b4298298c8b81dc16dc21f5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/947c03e48c4be7485f1547817f890c53.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291e4e0dc7974f2ce1b59620e3ec0232.png)
(3)如图3,斜三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e168672b47d7e64dc1b404f8882c7dcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6899bf9cadae2ccdb14cbc87d4f280ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa84da7ead562cffd02afd5940f8aa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1654dfe63f11563eadbaee32dae7b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0cebc1b9472488bfb8f0db1c723fef5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f64fa38725c136504f723019a18dc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93fa313adc4ac7608ba9449fd755212.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e8d4017e1a37acb0c8e00508be472b2.png)
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解题方法
9 . 记
的内角A,B,C的对边分别为a,b,c,已知
.
(1)证明:
;
(2)若
,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f73789e156d750cb54fe27ce4b04712.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a70d8f920d57c9c3f9cbffaf45c4055.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e65397f11ea8af736f38debadf420c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc8c65bea2c80af038768b74250c694e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
您最近一年使用:0次
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10 . 对于平面向量
,定义“
变换”:
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8560ca9023cf64637ce1467f338556bd.png)
(1)若向量
,
,求
;
(2)已知
,
,且
与
不平行,
,
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d128ae3e21294e2eac5bcc775ccfb03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a18fd5445fb8a04b925a2745a56f613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fddd9dc1110e60973b7b9e43bb1f9d15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8560ca9023cf64637ce1467f338556bd.png)
(1)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea462b0382581d99c8bba51d9b79f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3e186ebc624ebacde9a03b96289f1ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2e900404ba71110c5861ced9634646f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22601439d36b6a93453d738c2b803eb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc499d2e731df31957eeaa355bfbac4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fc9656d8286c4d6fa309d6ae347c89e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a63cf7e5f25165ccf0e24d32add179ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a176f300a2462e4f1ffef99d30c21e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e719e667f2783febbec38dea080b98.png)
您最近一年使用:0次