Solution:
The points $(4,7,8),(2,3,4)$ and $(-1,-2,1),(1,2,5)$.
Consider $A B$ be the line joining the points, $(4,7,8),(2,3,4)$ and $C D$ be the line through the points $(-1,-2$, 1), $(1,2,5)$.
So now,
The direction ratios, $a_{1}, b_{1}, c_{1}$ of $A B$ are
$(2-4),(3-7),(4-8)=-2,-4,-4$
Direction ratios, $\mathrm{a}_{2}, \mathrm{~b}_{2}, \mathrm{c}_{2}$ of $\mathrm{CD}$ are
$(1-(-1)),(2-(-2)),(5-1)=2,4,4$
Then $\mathrm{AB}$ will be parallel to $\mathrm{CD}$, if
$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
Therefore, $a_{1} / a_{2}=-2 / 2=-1$
$\begin{array}{l}
\mathrm{b}_{1} / \mathrm{b}_{2}=-4 / 4=-1 \\
\mathrm{c}_{1} / \mathrm{c}_{2}=-4 / 4=-1
\end{array}$
Therefore, we can say that,
$\begin{array}{c}
\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}} \\
-1=-1=-1
\end{array}$
As a result, $\mathrm{AB}$ is parallel to $\mathrm{CD}$ where the line through the points $(4,7,8),(2,3,4)$ is parallel to the line through the points $(-1,-2,1),(1,2,5)$