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Let -> aand -> bbe two unit vectors a...

Let ` -> a`and ` -> b`be two unit vectors and is the angle between them. Then ` -> a+ -> b`is a unit vector if(A) `theta=pi/4` (B) `theta=pi/3` (C) `theta=pi/2` (D) `theta=(2pi)/3`

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We are given, `veca,vecb and veca+vecb` all are unit vector which means
`|veca| = |vecb| = |veca+vecb| = 1`
Now, `|veca+vecb| = 1`
`=>(|veca+vecb|)^2 = 1`
`=>(|veca+vecb|)^2 = 1`
`=>(veca+vecb).(veca+vecb) = 1`
`=>veca.veca +veca.vecb + vecb.veca+vecb.vecb= 1`
`=>|a|^2+2veca.vecb+|b|^2=1`
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