Question

Direction vector of a line perpendicular to a given line

Answer 1

Answer:

If the equation of a line is

ax + by + c = 0

then (a, b) is a vector normal to the line.

That is, (a, b) is a direction vector for a line perpendicular to the given line.

To see this, notice that the slope of the given line is -a/b.  So the slope of a perpendicular line is b/a.  The vector (a,b) has this slope, so it's what we want.