Question: (a) (4 points) For the path parameterized by \(\mathbf{r}(t)=t \mathbf{i}+\sin t \mathbf{j}+e^{2 t} \mathbf{k}\), compute parametric equations for the tangent line at the point \(\left(\pi, 0, e^{2 \pi}\right)\).

(b) (4 points) For the surface \(S\) given by \(z=\sqrt{x^{2}+y^{2}}\), compute parametric equations for the tangent plane to the surface at \((3,4,5)\).

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