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

Let n^1  and  n^2 be the two unit vectors, then the sum isn¯  =  n^1 +  n^2or ns2  = n12+n22+2n1n2cosθ           = 1+1+2cosθsince it is given that ns is also a unit vector, therefore1 = 1+1+2cosθ  ⇒  cosθ = -12   ∴θ = 1200Now the difference vector is n^d  =  n^1 −  n^2 ornd2 = n12 +n22−2n1n2cosθ  = 1+1−2cos(1200)∴  nd2 = 2-2(-12) = 2+1 = 3 ⇒ nd = 3