- A) X = 13t, Y = T, Z = T

$\text { For the smooth curve } r ( t ) \text {, find the parametric equations for the line that is tangent to } r \text { at the given parameter value } t = t _ { 0 } \text {. }$
- $$\mathbf { r } ( \mathrm { t } ) = \left( 4 \mathrm { t } ^ { 2 } - 3 \mathrm { t } \right) \mathbf { i } + ( \mathrm { t } + 7 ) \mathbf { j } + \mathbf { k } ; \mathrm { t } _ { 0 } = 2$$

A) x = 13t, y = t, z = t
B) x = 10 + t, y = t, z = t
C) x = 10 + 13t, y = 9 + t, z = 1
D) x = 10 + 13t, y = 9 + t, z = 0