Let \hat{n}_{1} and \hat{n}_{2} are the two unit vectors, then the sum is

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

⇒ ⇒ \(\cos \theta = - \frac{1}{2}\) \ \ \(\theta = 120^\circ\)

Now the difference vector is \(\hat{\mathbf{n}}_d = \hat{\mathbf{n}}_1 - \hat{\mathbf{n}}_2\) or \(n_{d}^{2} = n_{1}^{2} + n_{2}^{2} - 2 n_{1} n_{2} \cos \theta = 1 + 1 - 2 \cos(120^{\circ})\)

\(n_{d}^{2} = 2 - 2(-1/2) = 2 + 1 = 3 \Rightarrow n_{d} = \sqrt{3}\)