1 . 若
都是单位向量,则下列结论一定正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8ccba3b87a8a48ac3dd5f72d00bdb1a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 对于任意向量
,下列命题中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/116e2e7116a7b5cd0a912ec0699ca017.png)
A.若![]() ![]() | B.![]() |
C.![]() | D.![]() |
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3 . 设
为非零向量,则“
”是“存在整数
,使得
”的( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd246148371f6f825f94e68480190f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243a6c8475337f0872477a8516fb8d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ced462f685c423ff4bcbf6544e69bd07.png)
A.充分而不必要条件 | B.必要而不充分条件 |
C.充分必要条件 | D.既不充分也不必要条件 |
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解题方法
4 . 已知同一平面内非零向量
,下列结论中正确个数的为( )
①若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ce380bce6978d2acd0742bed4e98e6.png)
②若
,则
不能作为此平面内的一组基底
③若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5aa846a5b7c96fe2ce665eb1ea5f0e.png)
④若
,则
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecfaf651f46c6915a3f463d67ec0e5c.png)
⑤
在
方向上的投影向量为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f057d8b12720e8841dad5cf78f1bf3ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96022a881e03e32d3483d997c3f170c6.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c9e602f8855225688f3c5f4c6a10d37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ce380bce6978d2acd0742bed4e98e6.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0fc4cd72b89a33bf68aa756a0c8d013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3908e03d141b78d56043b00617f900e3.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480e7839b807ca5c0c6c4028eba6c00c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa5aa846a5b7c96fe2ce665eb1ea5f0e.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42520c17641723a393ff87f0e7755a8f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58ce380bce6978d2acd0742bed4e98e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecfaf651f46c6915a3f463d67ec0e5c.png)
⑤
![](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/f057d8b12720e8841dad5cf78f1bf3ed.png)
A.0 | B.1 | C.2 | D.3 |
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解题方法
5 . 给出下列四个命题:
①若
,则对任意的非零向量
,都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414c4b7cbf90e2447c829e2feb24d8e5.png)
②若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95a60c8be97a2f7fdc2c306d4c52c1f.png)
③若
,
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a7e519edfac1c359d1f1a7a1940797.png)
④对任意向量
都有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53d9dd599297d984517d145e95b8e1f.png)
其中正确的命题个数是( )
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ac83b90b25c938f37b0c548af0c4d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414c4b7cbf90e2447c829e2feb24d8e5.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ac83b90b25c938f37b0c548af0c4d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/414c4b7cbf90e2447c829e2feb24d8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95a60c8be97a2f7fdc2c306d4c52c1f.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5244da74f8090bac8adb9f0fbf0fe4f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a8257a69f6d6e48f0696be859db61a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6a7e519edfac1c359d1f1a7a1940797.png)
④对任意向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79f0703f0b825571f321c7e2b29e1d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b53d9dd599297d984517d145e95b8e1f.png)
其中正确的命题个数是( )
A.3 | B.2 | C.1 | D.0 |
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