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

1/5(a+3b)-1/2(a-b)=1/5(3a+2b), [1/5-1/2-3/5]a=[2/5-3/5-1/2]b 9/10a=6/10b
3a=2b b=3/2a 所以向量a与b共线,
/a/:/b/ =2:3