已知向量a,b满足1/5（a+3b）-1/2(a-b)=1/5(3a+2b),求证：向量a与b共线,并求a的绝对值:b的绝对值

题目

已知向量a,b满足1/5（a+3b）-1/2(a-b)=1/5(3a+2b),求证：向量a与b共线,并求a的绝对值:b的绝对值

答案

1/5（a+3b）-1/2(a-b)=1/5(3a+2b)
=>a/5+3b/5-a/2+b/2=3a/5+2b/5
=>(1/5-1/2-3/5)a=(2/5-3/5-1/2)b /*把ab移两边*/
=>9a=7b
=>a=7/9 b
=>a与b共线,and |a|:|b|=7:9=7/9