Answer
$x=4+4t; y=3+2t; z=8+12t$
Work Step by Step
Since we know the velocity is:
$v(t)=r'(t)=\lt 2t,2,3t^2\gt$
and $v(2)=\lt 4,2,12 \gt$
The velocity components of $v$ are : $v_x=4,v_y=2,v_y=12$
So, the parametric equations are:
$x=(4)t+4=4+4t; y=(2) t+(3)=3+2t; z=(12)t+(8)=8+12t$
Hence, $x=4+4t; y=3+2t; z=8+12t$
