Explanation

(b)
$\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} = \left| \begin{matrix}
\widehat{\dot{\mathbf{i}}} & \widehat{\dot{\mathbf{j}}} & \widehat{\mathbf{k}} \\
1 & 1 & 0 \\
0 & 1 & 1
\end{matrix} \right| = \widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}$
∴ Unit vector
$= \pm \frac{\overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}}}{\left| \overrightarrow{\mathbf{a}} \times \overrightarrow{\mathbf{b}} \right|} = \pm \frac{\widehat{\dot{\mathbf{i}}} - \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}}{1^{2} + 1^{2} + 1^{2}}$
$= \pm \frac{\widehat{\dot{\mathbf{i}}} + \widehat{\dot{\mathbf{j}}} + \widehat{\mathbf{k}}}{\sqrt{3}}$
So, there are two perpendicular vectors of unit length.