Question

3. (5 points) (a): Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

$$ x=e^{-t} \cos t, \quad y=e^{-t} \sin t, \quad z=e^{-t} ; \quad(1,0,1) $$

(b): Find the unit tangent vector \(\mathbf{T}\), the principal unit normal \(\mathbf{N}\), and the curvature \(\kappa\) for the space curve,

$$ \mathbf{r}(t)=<3 3="" 4="" sin="" cos="" t="">$$

Answer 1