\[ r(t) = \begin{bmatrix} 3 \cos t + 2 \sin t \\ - 2 \sin t \\ 4 \cos t + \sin t \end{bmatrix} \]

Let \( r(t) \) be the parametric vector defined above. What is the area enclosed by the closed curve that \( r(t) \) traces over \( [0, 2 \pi ] \), in the plane that \( r(t) \) lies in?

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