S6.803.12.5.9 are lines parallel?

[karush]

$\tiny{s6.803.12.5.9}$
$\textsf{Is the line through $( -4,-6,1)$
and $(-2,0,-3)$ parallel}\\$
$\textsf{to the line through $( 10,18,4)$
and $(5,3,14)$? }\\$
$\textit{presume, convert to vectors first?}$
\begin{align}
\displaystyle
{}&={}\\
\end{align}

 

[MarkFL]

A vector parallel to the first line is:

\(\displaystyle \langle -4-(-2),-6-0,1-(-3)\rangle=\langle -2,-6,4\rangle=-2\langle 1,3,-2\rangle\)

A vector parallel to the second line is:

\(\displaystyle \langle 10-5,18-3,4-14\rangle=\langle 5,15,-10\rangle=5\langle 1,3,-2\rangle\)

So, yes, the two given lines are parallel. :D