Answer
$r=\lt2,14-3t,-10+9t\gt$
and
$x=2t,y=14-3t,z=-10+9t $
Work Step by Step
Equation of the line is given by $r=r_0+tv$
$r=(0,14,-10) $
Thus, the vector equation of the line is
$r=(0,14,-10)+t\lt2,-3,9\gt$
$r=\lt2,14-3t,-10+9t\gt$
Hence, the parametric equations are:
$x=2t,y=14-3t,z=-10+9t $