Find an Equation for the Line Tangent to the Given $$\vec { r } ( t ) = \left\langle e ^ { t } , \cos ( t ) , t \right\rangle , ( 1,1,0 )$$

Multiple Choice

Find an equation for the line tangent to the given curve at the specified point. $$\vec { r } ( t ) = \left\langle e ^ { t } , \cos ( t ) , t \right\rangle , ( 1,1,0 )$$

A) $\vec { T } ( t ) = \langle 1,1,0 \rangle + t \langle 1,0,1 \rangle$
B) $\vec { T } ( t ) = \left\langle 0 , e ^ { 2 } , 1 \right\rangle + t \left\langle 0 , e ^ { 2 } , 1 \right\rangle$
C) $\vec { T } ( t ) = \left\langle 0 , e ^ { 2 } , 1 \right\rangle + t \left\langle 1,2 e ^ { 2 } , \frac { \pi } { 2 } \right\rangle$
D) $\vec { T } ( t ) = \left\langle 1,2 e ^ { 2 } , 0 \right\rangle + t \left\langle 0 , e ^ { 2 } , 1 \right\rangle$