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解题方法
1 . 已知正方体的棱长为
,点
满足
,其中
,
为棱
的中点,则下列说法正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9dd1458186cfbdf0701ba835572721.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82191560610f148b24fdb3470f99407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
A.若![]() ![]() ![]() ![]() |
B.当![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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2 . 已知正方体
的棱长为1,点P满足
,其中
,
,点E、F分别是
、
的中点,下列选项不正确 的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac6b545127bd51036a5a7b0d3cd5b320.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
A.当![]() ![]() |
B.当![]() ![]() |
C.存在![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() |
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3 . 关于平面向量,下列说法正确的是( )
A.若![]() ![]() |
B.在平行四边形![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若四边形![]() ![]() ![]() ![]() |
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4 . 如图,
中,
,
,
与
交于点
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16fc30fe92ea3aa9a6e2612967c34a82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7444ac79b9fd0dcae522e1975f21f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 若向量
是三个不共线向量,则下列关于
的方程判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae951e0bb5a2a406f1572fc1e4964265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.方程![]() |
B.方程![]() ![]() |
C.方程![]() |
D.方程![]() ![]() |
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6 . 在
中,P,Q分别为边AC,BC上一点,BP,AQ交于点D,且满足
,
,
,
,则下列结论正确的为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8ce37bbe-c0f7-4278-8ce9-06f484ad459c.png?resizew=156)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a7abc23309378495afc6abd62cf180f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/653f99f9d3f299793f8a9c490acf0922.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e454a74fd8051bc7be466e5ad6bc1c7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab4a611415c6f78c87c4deaed8cdb5e9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/14/8ce37bbe-c0f7-4278-8ce9-06f484ad459c.png?resizew=156)
A.若![]() ![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() |
D.![]() |
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7 . 在棱长为1的正方体
中,点P满足
,
,
,则以下说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f102d05748b5cdec85905b097264c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cee72261f6901e62dfd0ffe547406544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34e2e01346f60857ff635bb766802e57.png)
A.当![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() ![]() |
D.当点P落在以![]() ![]() ![]() ![]() |
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解题方法
8 . 如图,设
,且
,当
时,定义平面坐标系
为
的斜坐标系,在
的斜坐标系中,任意一点
的斜坐标这样定义:设
,
是分别与
轴,
轴正方向相同的单位向量,若
,记
,则下列结论中正确的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/516f8ace-147e-4e42-a25b-7f0bc75507cb.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f55b8836b41be612a52ca9caf97006.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d26c9fc8cfa002f40ea3908575c8ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ca0fbe6fbda5d57855ee78caa84bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b28baf17059c56ee9ad1ae4814acd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b04618e5b2db68f2de6ba68972c505c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b257fe21a91d22e853b1642c9d44647.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/beeef1949e7c1280442c22fb01dd8e75.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/18/516f8ace-147e-4e42-a25b-7f0bc75507cb.png?resizew=185)
A.设![]() ![]() ![]() ![]() ![]() |
B.设![]() ![]() |
C.设![]() ![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() ![]() ![]() |
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9 . 已知平面非零向量
,
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
A.若![]() ![]() ![]() |
B.若存在非零向量![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.设![]() ![]() ![]() ![]() ![]() ![]() |
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解题方法
10 . 如图,已知点
是平行四边形
的边
的中点,点
在线段
上,且满足
,其中数列
是首项为1的数列,
是数列
的前
项和,则下列结论正确的是( )
![](https://img.xkw.com/dksih/QBM/2021/10/24/2841958141263872/2923167029788672/STEM/0f7dca0df6964f5b8b35ae2ddeda1b64.png?resizew=242)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](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/8e1d1264d831a01b85790aa827ba9694.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1692bed7376dc331d5e946e577224eca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08eb71ecf8d733b6932f4680874dbbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63d471926f7b27322d90c82b9ce21d3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://img.xkw.com/dksih/QBM/2021/10/24/2841958141263872/2923167029788672/STEM/0f7dca0df6964f5b8b35ae2ddeda1b64.png?resizew=242)
A.![]() | B.数列![]() |
C.![]() | D.![]() |
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