(1)ab=|a||b|cos=2根号3cos150=-3
|a+2b|=根号[(a+2b)(a+2b)]=根号(a^2+4ab+4b^2)=根号(|a|^2+4|b|^2-12)=根号7
(2)若a-b与a垂直,则(a-b)a=a^2-ab=|a|^2-ab=3-ab=0ab=3
cos=(ab)/(|a||b|)=3/(2根号3)=根号3/2=30度.