JEE Advanced 2022 · Paper 2, Physics question 1

A particle of mass 1 kg is subjected to a force which depends on the position as $\vec F = -k(x\hat i + y\hat j)\ \mathrm{kg\,m\,s^{-2}}$ with $k = 1\ \mathrm{kg\,s^{-2}}$. At time $t = 0$, the particle's position $\vec r = \left(\frac{1}{\sqrt2}\hat i + \sqrt2\hat j\right)$ m and its velocity $\vec v = \left(-\sqrt2\hat i + \sqrt2\hat j + \frac2\pi\hat k\right)\ \mathrm{m\,s^{-1}}$. Let $v_x$ and $v_y$ denote the $x$ and the $y$ components of the particle's velocity, respectively. Ignore gravity. When $z = 0.5$ m, the value of $(x v_y - y v_x)$ is _____ $\mathrm{m^2s^{-1}}$.