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SCALCET$913\mathrm{.}2\mathrm{.}030.$EP$.$

Consider the curve $r(t)=($:$6cos(t),6sin(t),e^t$:$),0t.$

Find $r^{\text{'}}(t).$

$r^{\text{'}}(t)=$

Consider the plane $\sqrt[\phantom{2}]{3}xy=1.$ Determine the normal vector $n$ of the plane.

$n=$

Find the point on the curve $r(t)=($:$6cos(t),6sin(t),e^t$:$),0t,$ where the tangent line is parallel to the plane $\sqrt[\phantom{2}]{3}xy=1.$