已知向量
.
(1)若
,求证:
;
(2)若向量
共线,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec3a1c2de9999ecc540e3e463fc2d776.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f02fede76ba43141bafdb8e40963235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
(2)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b172cf8d898883d82e973f28c3c3a3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6369cd1db768436809404b1f3c4132c0.png)
更新时间:2023-07-22 22:21:25
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解答题-计算题
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【推荐1】已知
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(1)化简
;
(2)若
,求
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(1)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb07c5dc0c3e853cbdf97179bc60dfb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/794f2c6bd63355105d179d11306a9cae.png)
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【推荐2】已知
,求
和
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e182e4d9e4e7a10f858201d24abd606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d66c03d4ca06819a6ce7fc8ea6de0f0.png)
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【推荐1】已知向量
.
(1)若
与
共线,求
;
(2)若
在
上的投影为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f104cf8bbaabc5e57b6554e0895692.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e07882aa0d4087bd4e551dbfa437e31d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9db9373e74ecf5d63ad98afe66aa4ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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【推荐2】平面内给定两个向量
,
.
(1)求
;
(2)若
,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f89d9cd2d59f0d0366e64469ad376b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67584e2063b8190b096eda30501e596b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/022030927a837bf502d1847da4e15dc9.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/963c419fc22125db316ecd3dd3a83a84.png)
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【推荐1】已知
,
,
,直线
经过A,B两点,我们把向量
以及与它平行的非零向量都称为直线
的方向向量,把与直线
垂直的向量称为直线
的法向量,则向量
在直线
的法向量上的投影向量的模就是点
到直线
的距离.
(1)求直线
的一个法向量;
(2)运用上述方法,求点
到直线
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a26e951d6d2369e8da79a793a93a66a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc27522334072c7f41cc482c1c67e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9404ad60dd25cb0df6c37032d50b72ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abcb5d89b04570ceda2c29e11cb27a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/454a02d14e3371707f979ea0cd7b9412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)运用上述方法,求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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【推荐2】已知直线
为参数,
,以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,圆
的极坐标方程为
,圆
与极轴和直线
分别交于点
,点
(异于坐标原点).
(1)写出点
的极坐标及圆
的直角坐标方程;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7ea2c9b5aef8a6b1341e6c4bf0b171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b6d2853ae57f4d2c3b5a0ac6fd4a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120c0192f3a2e1bf69348350a710b737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad28cf8dd484ddea92cb200a50dcf60.png)
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【推荐3】已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/18/89df90fa-daef-4937-a8ce-85d0d70e72d7.png?resizew=172)
(1)已知
,在所给直角坐标系中标出A,B两点的位置;
(2)求
;
(3)求
;
(4)求
在
方向上的投影的数量.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aa0f7263e945c33b42169f2b9b26da5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/18/89df90fa-daef-4937-a8ce-85d0d70e72d7.png?resizew=172)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b95a58a71ef3f33901dc8d025b0b0cf9.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/888f4bf0aba0461134c5e632bcee6bab.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16111d1425b87ba82ea6a706d1dfb3ef.png)
(4)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
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【推荐1】已知向量![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2d3d2c361d6432c26870316645a266.png)
(1)已知
且
,求![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
(2)已知
,且
,求向量
与向量
的夹角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db2d3d2c361d6432c26870316645a266.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5ebf6501c1606dbadd67cb5de19167f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dd43c3c9a578b91fe832c4c2477103c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8d5597259027974564a87ae3052e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba4f32ab362cc031157287f2aeaefa01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73a0b19e69be46452425916a0fcb49c9.png)
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【推荐2】已知向量
,
满足
,
,且
.
(1)求向量
的坐标;
(2)求向量
与
的夹角.
![](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/51547fd908ffdae4ba26822ae325b860.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8192ffdba85c4e57e851b1bf076c4e20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075e358bf8f0aab842e87ab3f0df903f.png)
(1)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
(2)求向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a2f4b1178f68bd147d1a2a6acd04435.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94075193c11fe43f2396cff5a485054.png)
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