Question: Show that the curve with vector equation \(\vec{r}=\left( 2{{\cos }^{2}}t,\sin 2t,2\sin t \right)\) is the curve of intersection of the surfaces \({{\left( x-1 \right)}^{2}}+{{y}^{2}}=1\) and \({{x}^{2}}+{{y}^{2}}+{{z}^{2}}=4\). Use this fact to sketch the curve.