Answer
$x= 3, y= 2-4t , z=1+2t$
Work Step by Step
If $P= (x_{1},y_{1},z_{1})$ and $\textbf{v}=a\hat{i}+b\hat{j}+c\hat{k}$,
Then, $x= x_{1}+at,y=y_{1}+bt$ and $ z= z_{1}+bt.$
In this case, P=(3,2,1) and $\textbf{v}= <0,-4,2>.$
Therefore, the parametric equations are
$x= 3+ 0t= 3, y= 2+(-4\times t)= 2-4t, z= 1+2t$
