Question

which pair of lines are perpendicular?

a) 2x + 3y - 7=0, -3x - 2y + 2=0

b) 2x - 3y + 2=0, 5x - 7y + 2=0

c) -4x + y - 3=0, x + 4y=0

d) -5x + y + 1=0, 5x + y + 1=0


Please explain. I know we have to use the dot product :3

Answer 1

for any ax + by + c = 0 , the direction vector of the normal is (a,b)
If the normals are perpendicular, then obviously the line are perpendicular, so ...

a)
normal to first line is (2,3)
normal to 2nd line is (-3,-2)
dot product = -6 - 6 ≠ 0
so the lines are NOT perpendicular.

do the others the same way.
If you get a dot product of zero , they are perpendicular.