Can a rectangular component of a vector be greater than the vector itself ?

Explanation

No. For illustration. The rectangular componet of a vectro ` vec A` along x-direction and y-direction are ` A_(x) =A cos and A_(y) =A sin theta`, where theta` is the
angle which ` vec A` makes with x-axis. As ` sin teta and cos theta`, form differnt angles, can take vealues between - 1 to + 1` so the magnitudes of both ` A_(x) and A_(y)` can never be grater then `A`.