Answer
$${\bf{v}} = 4{\bf{i}} + 4\sqrt 3 {\bf{j}}$$
Work Step by Step
$$\eqalign{
& \left\| {\bf{v}} \right\| = 8,{\text{ }}\theta = 60^\circ \cr
& {\text{The components of }}{\bf{v}}{\text{ are given by }} \cr
& {\bf{v}} = \left\| {\bf{v}} \right\|\left( {\cos \theta {\bf{i}} + \sin \theta {\bf{j}}} \right) \cr
& {\text{Then,}} \cr
& {\bf{v}} = 8\left( {\cos 60^\circ {\bf{i}} + \sin 60^\circ {\bf{j}}} \right) \cr
& {\text{Simplifying}} \cr
& {\bf{v}} = 8\left( {\frac{1}{2}{\bf{i}} + \frac{{\sqrt 3 }}{2}{\bf{j}}} \right) \cr
& {\bf{v}} = 4{\bf{i}} + 4\sqrt 3 {\bf{j}} \cr} $$
