Solution:
Given that
The points $(1,-1,2),(3,4,-2)$ and $(0,3,2),(3,5,6)$.
Let’s consider $A B$ be the line joining the points, $(1,-1,2)$ and $(3,4,-2)$, and $C D$ be the line through the points $(0,$, $3,2)$ and $(3,5,6)$.
So now,
Direction ratios, $a_{1}, b_{1}, c_{1}$ of $A B$ are
$(3-1),(4-(-1)),(-2-2)=2,5,-4$
In the similar way,
The direction ratios, $a_{2}, b_{2}, c_{2}$ of $C D$ are
$(3-0),(5-3),(6-2)=3,2,4$
Therefore, $A B$ and $C D$ will be perpendicular to each other, if $a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0$
$\begin{array}{l}
a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=2(3)+5(2)+4(-4) \\
=6+10-16 \\
=0
\end{array}$
As a result, $\mathrm{AB}$ and $\mathrm{CD}$ are perpendicular to each other.