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If the sum of two unit vectors is a unit vector, then the magnitude of their diffierence is |
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Answer» `sqrt2` Also, `|hata|=|hatb|=|hata+hatb| =1` So, `Delta OAB` is an equilateral triangle. `therefore |OA|=|hata| = 1= |-hatb|= |AB'|` THUS, `Delta OAB' ` is an isosceles triangle. `angle AB' O= angleAOB'=30^(@)` `and angle BOB' = angleBOA+angleAOB' = 90^(@)` `therefore " In " DeltaBOB', |B B'|^(2)=|OB|^(2)+|OB' |^(2)` `rArr 2^(2) = |hata + hatb|^(2) + |hata-hatb|^(2)` `rArr |hata - hatb|=SQRT(4-1)=sqrt(3)` |
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