Let AB be the line through the points, (4, 7, 8) and (2, 3, 4), and CD be the line through the points,

Let AB be the line through the points, (4, 7, 8) and (2, 3, 4), and CD be the line through the points, (−1, −2, 1) and (1, 2, 5).

The directions ratios, $a_{1}, b_{1}, c_{1}$, of $A B$ are $(2-4),(3-7)$, and $(4-8)$ i.e., $-2,-4$, and $-4$

The direction ratios, $a_{2}, b_{2}, c_{2}$, of CD are $(1-(-1)),(2-(-2))$, and $(5-1)$ i.e., 2,4, and 4 .

AB will be parallel to $\mathrm{CD}$, if $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

$\frac{a_{1}}{a_{2}}=\frac{-2}{2}=-1$

$\frac{b_{1}}{b_{2}}=\frac{-4}{4}=-1$

$\frac{c_{1}}{c_{2}}=\frac{-4}{4}=-1$

$\therefore \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

Thus, AB is parallel to CD.