[Math] Are two planes parallel when their direction vector is equal

Question

The vectors topic is getting really confusing and googling ispretty much useless since all the answers I've found are really complex.

are these two fictious planes below parallel?

Plane alpha:$r(xi +yj +zk)=10$
Plane beta : $r(xi +yj +zk)=15$

Edit: isnt the general equation for a plane $r(xi+yi+zk)=c$ ?

Answer 1

Two planes are said to be parallel when their normal vectors are parallel. And two vectors are said to be parallel if their cross product is zero.

In other words, the direction cosines of the normal vectors are proportional if they are parallel.

Hope this helps.