Find a Vector-Valued Function, Using the Given Parameter, to Represent $\begin{array}{l}\text { Surfaces }&\text { Parameter }\\z=x^{2}+y^{2}, z=81&x=9 \cos 8 \pi t\end{array}$

Multiple Choice

Find a vector-valued function, using the given parameter, to represent the intersection of the surfaces given below. $\begin{array}{l}\text { Surfaces }&\text { Parameter }\\z=x^{2}+y^{2}, z=81&x=9 \cos 8 \pi t\end{array}$

A) $\mathbf { r } ( t ) = 9 \mathbf { i } + 9 \sin 8 \pi \mathbf { j } + 9 \cos 8 \pi \mathbf { k }$
B) $\mathbf { r } ( t ) = 9 \cos 8 \pi \mathbf { i } + 9 \sin \pi \mathbf { j } + 81 \mathbf { k }$
C) $\mathbf { r } ( t ) = 9 \cos 8 \pi \mathbf { i } + 9 \sin 8 \pi \mathbf { j } + 9 \mathbf { k }$
D) $\mathbf { r } ( t ) = 9 \cos 8 \pi t \mathbf { i } + 81 \mathbf { j } + 9 \sin 8 \pi \mathbf { k }$
E) $\mathbf { r } ( t ) = 9 \cos 8 \pi \mathbf { i } + 9 \sin 8 \pi \mathbf { j } + 81 \mathbf { k }$