For the velocity field \(\vec{V}=A x \hat{i}-A y \hat{j}\), where \(A=2 \mathrm{~s}^{-1}\), which can be interpreted to represent flow in a corner, show that the parametric equations for particle motion are given by \(x_{p}=c_{1} e^{A t}\) and \(y_{p}=c_{2} e^{-A t}\). Obtain the equation for the pathline of the particle located at the point \((x, y)=(2,2)\) at the instant \(t=0\). Compare this pathline with the streamline through the same point.