A particle of mass 1 kg is subjected to a force which depends on the position as $\overrightarrow{F}=-k\left(x\hat{i}+y\hat{j}\right)$ ${\text{kg ms}}^{-2}$ with $k=1{\text{kg s}}^{-2}$. At time $t=0$, the particle's position is $\overrightarrow{r}=\frac{1}{\sqrt{2}}\hat{i}+\sqrt{2}\hat{j}$ m and its velocity is $\overrightarrow{v}=\{-\sqrt{2}\hat{i}+\sqrt{2}\hat{j}+\sqrt{2}\hat{k}$ ${\text{}ms}}^{-1}$. Let $v_x$ and $v_y$ denote the $x$ and $y$ components of the particle's velocity, respectively. Ignore gravity. When $z=0.5\text{m}$, the value of $(x{v}_y-y{v}_x)$ is _____ ${\text{m}}^2{\text{s}}^{-1}$.