Answer
The vectors $\vec{u}$ and $\vec{v}$ are not perpendicular.
Work Step by Step
$\vec{u}=\langle-2,6\rangle$ $,$ $\vec{v}=\langle4,2\rangle$
Find $\vec{u}\cdot\vec{v}$ by multiplying corresponding components and adding:
$\vec{u}\cdot\vec{v}=(-2)(4)+(6)(2)=-8+12=4$
Since the dot product of these two vectors is not equal to $0$, they are not perpendicular.
