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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 particle's 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 particle's velocity, respectively. Ignore gravity. When \(z=0.5 \mathrm{~m}\), the value of \(\left(x v_{y}-y v_{x}\right)\) is \(\mathrm{m}^{2} \mathrm{~s}^{-1}\). 📲PW App Link - https://bit.ly/YTAI_PWAP 🌐PW Website - https://www.pw.live