1、a*b=1*2*cos60°=1,|a+b|^2=(a+b)*(a+b)=|a|^2+2(a*b)+|b|^2=7,|a+b|=√7
(a+b)*a=|a|^2+(a*b)=2
a+b与a夹角的余弦等于(a+b)*a/(|a+b|*|a|)＝2/√7
2、|a+tb|^2=(a+tb)*(a+tb)=|a|^2+2t(a*b)+t^2*|b|^2=1+2t+4t^2=(2t+1/2)^2+3/4.当t=-1/4时,|a+tb|最小.
此时,(a+tb)*b=a*b+t(|b|^2)=1-1=0,所以a+tb与垂直.