O是正六边形
的中心,且
,在以A、B、C、D、E、F、O为端点的向量中:
![](https://img.xkw.com/dksih/QBM/2021/3/16/2679326601854976/2684215658274816/STEM/5f7fbd78ef594e86a1b3710a7951432b.png?resizew=142)
(1)与
相等的向量有_________ 个;
(2)与
互为负向量有__________ 个;
(3)与
平行的向量有个__________ 个.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9165d9bfbb0f0d19eb482c2a4c1b29b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d71baf26445d2aea407a9e250d856bf.png)
![](https://img.xkw.com/dksih/QBM/2021/3/16/2679326601854976/2684215658274816/STEM/5f7fbd78ef594e86a1b3710a7951432b.png?resizew=142)
(1)与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
(2)与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
(3)与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb573cc0f30d5c32cdad1510793f0e7b.png)
更新时间:2021-03-23 19:13:38
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填空题-单空题
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解题方法
【推荐1】下面关于向量的结论中,
(1)
;
(2)
;
(3)若
,则
;
(4)若向量
平移后,起点和终点的发生变化,所以
也发生变化;
(5)已知
、
、
、
四点满足任三点不共线,但四点共面,
是平面
外任一点,且
,则
.其中正确的序号为________ .
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16841ba647ca17f3430237c1a524a8f9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff7e9aa34228f5af074c6e2cdc01029.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd70c53abc3afb60393856afdaf376a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5072e817a6b9a062730d22af64a8314c.png)
(4)若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe35c91649a5bea2518387a2b36e0c0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe35c91649a5bea2518387a2b36e0c0d.png)
(5)已知
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/213c565ce9ffc74378516ef423b4f409.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2ad8b04e76f279435a68114408daf90.png)
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【推荐2】已知向量
=(2x,7),
=(6,x+4),当x=____ 时,
;当x=_____ 时,
且
.
![](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/58ce380bce6978d2acd0742bed4e98e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70facc9bc02af0867d248407bd317c05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/285736114f363b2c9c976668af4a1737.png)
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【推荐1】下列说法中:
①两个有共同起点且相等的向量,其终点一定相同;
②若
,则
;
③若非零向量
,
共线,则
;
④若向量
,则向量
,
共线;
⑤由于零向量的方向不确定,故其不能与任何向量平行;
其中正确的序号为_______________________ .
①两个有共同起点且相等的向量,其终点一定相同;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab14f1db85f43583c37c416c1bcacd67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b7ca4667865ebe617fa6539e8d11fd.png)
③若非零向量
![](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/e4b7ca4667865ebe617fa6539e8d11fd.png)
④若向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b7ca4667865ebe617fa6539e8d11fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
⑤由于零向量的方向不确定,故其不能与任何向量平行;
其中正确的序号为
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【推荐2】若非零向量
与
互为相反向量,给出下列结论:①
∥
;②
≠b;③|
|≠|
|;④
=-
.其中所有正确命题的序号为____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45ea1d522a3ebbf5f5d8d330fdbd1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b549e16842d85432dfb178dc0de58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45ea1d522a3ebbf5f5d8d330fdbd1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b549e16842d85432dfb178dc0de58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45ea1d522a3ebbf5f5d8d330fdbd1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45ea1d522a3ebbf5f5d8d330fdbd1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b549e16842d85432dfb178dc0de58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87b549e16842d85432dfb178dc0de58e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f45ea1d522a3ebbf5f5d8d330fdbd1e6.png)
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解题方法
【推荐1】在三角形ABC中,点D是AB的中点,且满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dd315a4f697285399eb924e7736116.png)
______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7996930735cf56f6cf736aa7c03c9e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9dd315a4f697285399eb924e7736116.png)
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