b
(b) Let \({\hat n_1}\) and \({\hat n_2}\) are the two unit vectors, then the sum is

\({\overrightarrow n _s} = {\hat n_1} + {\hat n_2}\) or 

\(n_s^2 = n_1^2 + n_2^2 + 2{n_1}{n_2}\cos \theta \)

\( = 1 + 1 + 2\cos \theta \)

Since it is given that \({n_s}\) is also a unit vector, therefore \(1 = 1 + 1 + 2\cos \theta \) 

\(⇒\) \(\cos \theta = - \frac{1}{2}\) 

\(\therefore \theta = 120^\circ \)

Now the difference vector is \({\hat n_d} = {\hat n_1} - {\hat n_2}\) or 

\(n_d^2 = n_1^2 + n_2^2 - 2{n_1}{n_2}\cos \theta \)

\( = 1 + 1 - 2\cos (120^\circ )\)

\(n_d^2 = 2 - 2( - 1/2) = 2 + 1 = 3\)

\( \Rightarrow \,\,{n_d} = \sqrt 3 \)