Answer
$x=1+3t, y=2t, z= -2-3t$
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}+ct.$
Here, P=(1,0,-2) and $\textbf{v}= <3,2,-3>.$
Therefore, the parametric equations are
$x= 1+3t, y=0+2t=2t, z= -2+(-3\times t)= -2-3t$
