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

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Answer 1 · 2017-05-25T11:20:32

$|hata+hatb| =√3$

$=>sqrt(abshata^2+abshatb^2+2abshataabshatbcostheta)=sqrt3$

$=>sqrt(1^2+1^2+2xx1xx1costheta)=sqrt3$

[ $abshata=1 and abs hatb=1$ as they are unit vector]

$=>1^2+1^2+2xx1xx1costheta=3$

$=>costheta=(3-2)/2=1/2=cos60^@$

$=>theta=60^@$

Now

$|hata -hat b|$

$=sqrt(abshata^2+abshatb^2+2abshataabshatbcos(pi-theta))$

$=>sqrt(1^2+1^2-2xx1xx1costheta)$

$=>sqrt(1^2+1^2-2xx1xx1cos60^@$

$=>sqrt(1^2+1^2-2xx1xx1xx1/2)=1$

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