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A particle of mass \( 1 \mathrm{~kg} \) is subjected to a force which depends on the position as with \( \vec{F}=-k(x \hat{i}+y \hat{j}) \mathrm{kg} \mathrm{ms}^{-2} \). At time \( t=0 \), the particles position \( \vec{r}=\left(\frac{1}{\sqrt{2}} \hat{i}+\sqrt{2} \hat{j}\right) \mathrm{m} \) and its velocity \( \vec{v}=\left(-\sqrt{2} \hat{i}+\sqrt{2} \hat{j}+\frac{2}{\pi} \hat{k}\right) \mathrm{ms}^{-1} \). Let \( v_{x} \) and \( v_{y} \) denote the \( x \) and the \( y \) components of the particles velocity, respectively. Ignore gravity. When \( z=0.5 \mathrm{~m} \), the value of \( \left(x v_{y}-y v_{x}\right) \) is \( \mathrm{m}^{2} \mathrm{~s}^{-1} \).
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