1 . 定义:对于两个非零向量
和
,如果存在不全为零的常数
、
,使
,那么称
和
是线性相关的,否则称
和
是线性无关的.已知
,
,试判断
与
的线性关系(相关还是无关),并证明你的结论.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf611ba33980c2b94067406cc3804a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c76d58f076f37bfb0a7200ecb7d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/647f6682e4de215dce541a013c334a68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf611ba33980c2b94067406cc3804a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c76d58f076f37bfb0a7200ecb7d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf611ba33980c2b94067406cc3804a39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c18c76d58f076f37bfb0a7200ecb7d0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dd379c624402d9206303afb1fd8b45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ca94e7c25b02aefacbcb095daa2f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/969604545902c9a66549a4a44ec3a3c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90ab17fd4247cdd710c363d5d3fbc5bd.png)
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2019高三·全国·专题练习
2 . 已知点O为坐标原点,A(0,2),B(4,6),
=
+![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f576518d6128fa051538b1917a9e38a.png)
(1)求点M在第二或第三象限的充要条件;
(2)求证:当
=1时,不论
为何实数,A,B,M三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12de88a7bce3bae0a16a7d3512ace417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b946c9ee1e609e527dbfa5bf60907370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f576518d6128fa051538b1917a9e38a.png)
(1)求点M在第二或第三象限的充要条件;
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02d4a0302a58089408976b9e4ff561f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fcbfda6dc1c18aba4f8c0bcd3d6422.png)
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2012·陕西·三模
3 . 已知
为坐标原点,
,
.
(1)求点
在第二象限或第三象限的充要条件;
(2)求证:当
时,不论
为何实数,
三点都共线;
(3)若
,求当点
为
的平分线上点时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89d96d9ac8bb18e50947ef9491a84ad3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7187af095f3e5a0b50518fc1073c43f7.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)求证:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b517486a10c8e2ce5ba7024c2b06681e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fcbfda6dc1c18aba4f8c0bcd3d6422.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04edaa9114516efcd8ae9fe47785582e.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae8a6d5572ba0f1449578a4bd7930e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/664cc63a58f1b2e0b94d2cae5c6ba5de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4fcbfda6dc1c18aba4f8c0bcd3d6422.png)
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