Compute the cross product of the vector functions $r_1\left(t\right)=\left(x_1\left(t\right),y_1\left(t\right)\right)\mathrm{and}\left(r_2\left(t\right)=x_2\left(t\right),y_2\left(t\right)\right)$by thinking of ${\mathrm{ℝ}}^2$ as the xy-plane in ${\mathrm{ℝ}}^3.$That is, let $r_1\left(t\right)=\left(x_1\left(t\right),y_1\left(t\right),0\right)\mathrm{and}{r}_2\left(t\right)=\left(x_2\left(t\right),y_2\left(t\right),0\right),$and take the cross product of these vector functions.

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