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

Solution :
Let the components of $$\overrightarrow A $$ make angles $$\alpha ,\beta $$  and $$\gamma $$ with $$x,y$$  and $$z$$-axis respectively then $$\alpha = \beta = \gamma $$   and
$$\eqalign{ & {\cos ^2}\alpha + {\cos ^2}\beta + {\cos ^2}\gamma = 1 \cr & \Rightarrow 3{\cos ^2}\alpha = 1 \Rightarrow \cos \alpha = \frac{1}{{\sqrt 3 }} \cr & \therefore {A_x} = {A_y} = {A_z} = A\cos \alpha = \frac{A}{{\sqrt 3 }} \cr} $$