a
(a) Let the components of \(\overrightarrow A \) makes angles \(\alpha ,\,\beta \) and \(\gamma \) with \(x, y\) and \(z\) axis respectively then \(\alpha = \beta = \gamma \)

\({\cos ^2}\alpha + {\cos ^2}\beta + {\cos ^2}\gamma = 1\)

\( \Rightarrow 3{\cos ^2}\alpha = 1\) \(⇒ \cos \alpha = \frac{1}{{\sqrt 3 }}\)

\(\therefore \,\,\,{A_x} = {A_y} = {A_z} = A\cos \alpha = \frac{A}{{\sqrt 3 }}\)