Question

determine whether the planes are parallel, octagonal or neither

a. 4x + 5y + z = -1
3x + 5y - 37z = -3


b. 2x - y - 3z = -5
-2x - 6y - z = 3

Answer 1

I think you mean orthogonal not octagonal

a.
vector normal (perpendicular to) first plane 4 i + 5 j +1 k
second plane 3 i + 5 j -37 z
find the dot or cross product
dot is easier A dot B = |A||B| cos angle between
if cos is 0, they are othogonal because cos 90 degrees is 0
if cos is 1 or -1 they are parallel
in this case
dot product = 12 + 25 - 37
= ZERO
angle is 90 degrees, They are orthoganal
now you do the next one.