1.

If the sum of two unit vectors is a unit vector, then the magnitude of their diffierence is

Answer»

`sqrt2`
`sqrt3`
`sqrt5`
`sqrt7`

Solution :`OA = HATA , Ab = hatbOB = hata + hatb`

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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