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

Let n^1 and n^2 are the two unit vectors, then the sum isn→s=n^1+n^2 Magnitude of n→s is given by ns2=n12+n22+2n1n2cos⁡θ=1+1+2cos⁡θSince it is given that ns is also a unit vector, therefore1=1+1+2cos⁡θ⇒cos⁡θ=−12∴θ=120∘Now the difference vector is    n^d=n^1−n^2 Magnitude of  n^d  is given by     nd2=n12+n22−2n1n2cos⁡θ=1+1−2cos⁡120∘⇒nd2=2−2(−1/2)=2+1=3⇒nd=3