- $$r ( t ) = ( 10 \sin t ) i - ( 3 \cos 3 t ) j + e ^ { - 8 t _ { k } } \mathbf { k } ; t _ { 0 } = 0$$

Multiple Choice

$\text { For the smooth curve } r ( t ) \text {, find the parametric equations for the line that is tangent to } r \text { at the given parameter value } t = t _ { 0 } \text {. }$
- $$r ( t ) = ( 10 \sin t ) i - ( 3 \cos 3 t ) j + e ^ { - 8 t _ { k } } \mathbf { k } ; t _ { 0 } = 0$$

A) x = 10, y = -3t, z = -8 + t
B) x = 10t, y = -3, z = 1 - t
C) x = 10t, y = 3, z = 1 + t
D) x = 10t, y = -3, z = 1 - 8t