由题意,|a-2b|^2=(a-2b)·(a-2b)=|a|^2+4|b|^2-4a·b=1------(1)
|2a+3b|^2=(2a+3b)·(2a+3b)=4|a|^2+9|b|^2+12a·b=1/9-----(2)
(1)*3+(2)得:7|a|^2+21|b|^2=28/9,即:|a|^2+3|b|^2=4/9,代入(1)得:
4/9-3|b|^2+4|b|^2-1=4a·b,即:a·b=(|b|^2-5/9)/4,故:
(5a-3b)·(a-9b)=5|a|^2+27|b|^2-45a·b-3a·b=5(4/9-3|b|^2)+27|b|^2-48*(|b|^2-5/9)/4
=20/9-15|b|^2+27|b|^2-12|b|^2+60/9=80/9