What is the standard form for the resolution of a vector having magnitude ‘a’ and is inclined at an angle $\theta$ to the X axis?

The correct answer is $a(\cos \theta \widehat{ı}+\sin \theta \widehat{j})$. This is obtained by constructing a right-angled triangle with the distance of the point from the origin with either of the axes and then finding out the corresponding values for X and Y components.