Answer
$\lt 12,9,-1 \gt$
Work Step by Step
The line passing through containing the point $P(p,q,r)$ and parallel to the normal vector $n=\lt a,b,c\gt$ is expressed by the parametric equations as follows:
$x=p+at; y=q+bt; z=r+ct$
Here, $t$ is any real number.
Given: $x=1-t; y=2+t; z=-3t$
Let us consider $n=\overrightarrow {PQ} \times \overrightarrow {PR}$
$\overrightarrow {PQ} =\lt 2,-3,-3 \gt$ and $\overrightarrow {QR} =\lt -1,1,-3 \gt$
Here, the normal vector $n=\overrightarrow {PQ} \times \overrightarrow {PR}$ can be calculated as follows:
$\hat{n}=\begin{vmatrix}i&j&k\\2&-3&-3\\-1&1&-3\end{vmatrix}=12\hat{i}+9 \hat{j}+(-1)\hat{k}$
or, $\hat{n}=\lt 12,9,-1 \gt$
