Answer
$b$ and $c$ are perpendicular. There are no parallel lines.
Slopes are same for parallel lines. Slope of the line perpendicular to a line with slope $m$ is $-\frac{1}{m}$.
Since the slopes of line $b$ and $c$ are negative reciprocals, line $b$ and line $c$ are perpendicular.
Work Step by Step
For line $a$, slope $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{3-1}{0-(-2)}=\frac{2}{2}=1$
For line $b$, $m=\frac{4-1}{6-4}=\frac{3}{2}$
For line $c$, $m=\frac{1-3}{4-1}=\frac{-2}{3}$
Slopes are same for parallel lines. Slope of the line perpendicular to a line with slope $m$ is $-\frac{1}{m}$.
Since the slopes of line $b$ and $c$ are negative reciprocals, line $b$ and line $c$ are perpendicular.
