Find the Line Tangent to the Surface Given by the Function

Multiple Choice

Find the line tangent to the surface given by the function at the specified point $P$ in the direction of the vector $\vec { u }$ $f ( x , y ) = x ^ { 3 } - x ^ { 2 } y , P = ( 1,2 ) , \vec { u } = \left\langle \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } \right\rangle$

A) $\vec { r } ( t ) = \left\langle 2 + \frac { 1 } { 2 } t , 2 + \frac { \sqrt { 3 } } { 2 } t , 3 + \left( 2 + \frac { \sqrt { 3 } } { 2 } \right) t \right\rangle$
B) $\vec { r } ( t ) = \left\langle 1 + \frac { \sqrt { 3 } } { 2 } t , 2 + \frac { 1 } { 2 } t , - 1 + ( 2 \sqrt { 3 } - 4 ) _ { t } \right\rangle$
C) $\vec { r } ( t ) = \left\langle 1 + \frac { \sqrt { 3 } } { 2 } t , 2 + \frac { 1 } { 2 } t , - 1 - \left( \frac { \sqrt { 3 } + 1 } { 2 } \right) t \right\rangle$
D) $\vec { r } ( t ) = \left\langle 1 + \frac { \sqrt { 3 } } { 2 } t , 2 + \frac { 1 } { 2 } t , - 1 - t \right\rangle$