When is the resolution of a vector required?

Any vector in an arbitrary direction can always be replaced by two (or three)

Explain the resolution of a vector in two dimensions. Explain the resolution of a vector into its perpendicular components.

$A$ vector in the $x-y$ plane makes an angle of $30^{\circ}$ with the $y$-axis. The magnitude of the $y$-component of the vector is $2 \sqrt{3}$. The magnitude of the $x$-component of the vector will be:

Two forces act on point $A$ along the sides $AC$ and $AB$ of a right-angled triangle $ABC$ (where $\angle A = 90^{\circ}$). The magnitudes of these forces are inversely proportional to the lengths of the sides $AC$ and $AB$ respectively. If $F_1 = 1/AC$ and $F_2 = 1/AB$,then the resultant of these forces is proportional to:

Explain the resolution of a vector in three dimensions.