|hata+hatb| =√3
=>sqrt(abshata^2+abshatb^2+2abshataabshatbcostheta)=sqrt3
=>sqrt(1^2+1^2+2xx1xx1costheta)=sqrt3
[ abshata=1 and abs hatb=1 as they are unit vector]
=>1^2+1^2+2xx1xx1costheta=3
=>costheta=(3-2)/2=1/2=cos60^@
=>theta=60^@
Now
|hata -hat b|
=sqrt(abshata^2+abshatb^2+2abshataabshatbcos(pi-theta))
=>sqrt(1^2+1^2-2xx1xx1costheta)
=>sqrt(1^2+1^2-2xx1xx1cos60^@
=>sqrt(1^2+1^2-2xx1xx1xx1/2)=1