Vector $\overrightarrow{A}$ makes equal angles with $x,y$ and $z$-axis. Value of its components (in terms of magnitude of $\overrightarrow{A}$) will be

Let the components of $\overrightarrow{A}$makes angles $\mathrm{\alpha },\mathrm{\beta }\mathrm{and}\mathrm{\gamma }$ with $\mathrm{x},\mathrm{y}\mathrm{and}\mathrm{z}$-axis respectively

then $\mathrm{\alpha }=\mathrm{\beta }=\mathrm{\gamma }$ 

$\begin{array}{l}{\cos }^2\mathrm{\alpha }+{\cos }^2\mathrm{\beta }+{\cos }^2\mathrm{\gamma }=1\\ \Rightarrow 3{\cos }^2\mathrm{\alpha }=1\Rightarrow \mathrm{cos\alpha }=\frac{1}{\sqrt{3}}\\ \therefore {\mathrm{A}}_{\mathrm{x}}={\mathrm{A}}_{\mathrm{y}}={\mathrm{A}}_{\mathrm{z}}=\mathrm{Acos\alpha }=\frac{\mathrm{A}}{\sqrt{3}}\end{array}$