Consider following parametric equations for a curve.

x $=$ e$2$t cos$(2$t$),$ y $=$ e$2$t sin$(2$t$),$ z $=$ e$2$t

Find r$($t$).$

Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

x $=$ e$2$t cos$(2$t$),$ y $=$ e$2$t sin$(2$t$),$ z $=$ e$2$t$,(1,0,1)$