Answer
${\text{Neither orthogonal, nor parallel}}$
Work Step by Step
$$\eqalign{
& {\bf{u}} = - \frac{1}{3}\left( {{\bf{i}} - 2{\bf{j}}} \right),{\text{ }}{\bf{v}} = 2{\bf{i}} - 4{\bf{j}} \cr
& {\bf{u}} = - \frac{1}{3}{\bf{i}} + \frac{2}{3}{\bf{j}} \cr
& {\text{Find }}{\bf{u}} \cdot {\bf{v}} \cr
& {\bf{u}} \cdot {\bf{v}} = \left( { - \frac{1}{3}{\bf{i}} + \frac{2}{3}{\bf{j}}} \right) \cdot \left( {2{\bf{i}} - 4{\bf{j}}} \right) \cr
& {\bf{u}} \cdot {\bf{v}} = \left( { - \frac{1}{3}} \right)\left( 2 \right) + \left( {\frac{2}{3}} \right)\left( { - 4} \right) \cr
& {\bf{u}} \cdot {\bf{v}} = - \frac{2}{3} - \frac{8}{3} \cr
& {\bf{u}} \cdot {\bf{v}} = - \frac{{10}}{3} \ne 0 \cr
& {\text{Therefore}}{\text{, the vectors are not orthogonal}}{\text{.}} \cr
& {\text{Neither orthogonal, nor parallel}} \cr} $$
