Answer
$(2,1)\cdot(1,-2)=0$
Work Step by Step
If the vectors are perpendicular, their dot product must be zero.
Dot product$=(2,1)\cdot(1,-2)=2(1)+1(-2)=2-2=0$.
Therefore, $2\textbf {i}+\textbf {j}$ and $\textbf {i}-2\textbf {j}$ are perpendicular.