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

The correct answer is $\mathrm{a}\left(\cos \mathrm{\theta }\mathrm{î}+\sin \mathrm{\theta }\widehat{\mathrm{j}}\right)$. 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.