Subject: Calculus 3
Given two lines determine whether the lines are parallel, intersecting, or skew. If intersecting, find point of intersection.
$L1: \frac{1}{2}(x-6) = \frac{1}{3}(y-12) = \frac{1}{7}(z-4)$
$L2: \frac{1}{8}(x-1)=\frac{1}{24}(y+3)=\frac{1}{28}(z-5)$
The answer in the back says they are parallel, however when I tried to solve it on my own I reached the conclusion that they are not parallel. I compared the directional vectors:
$\frac{1/2}{1/8} = \frac{1/3}{1/24} = \frac{1/7}{1/28}$
Simplifies to
$4 = 8 = 4$
Which means they are not parallel? Did I do this correctly or did I make a mistake?