If |hata+hatb| =√3 then |hata -hat b| is?

1 Answer
May 25, 2017

|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