(Solved): Consider the following curve. x=sin(3t),y=cos(3t),z=9t Using the given parametric equations, giv ...

Consider the following curve. $x=\sin (3t),y=?\cos (3t),z=9t$ Using the given parametric equations, give the corresponding vector equation $r(t)$. $r(t)=$ Find $r^{?}(t)$ and $?r^{?}(t)?$. $\begin{array}{c}{r}^{?}(t)=\\ ?r^{?}(t)?=\end{array}$ Find the equation of the normal plane of the given curve at the point $(0,1,3?)$. Now consider the osculating plane of the given curve at the point $(0,1,3?)$. Determine each of the following. $\begin{array}{r}\mathbf{T}(t)=\\ {\mathbf{T}}^{?}(t)=\\ ?{\mathbf{T}}^{?}(t)?=\\ \mathbf{N}(t)=\end{array}$ Find the equation of the osculating plane of the given curve at the point $(0,1,3?)$.