It's not a coincidence. In vector, usually denoted by
So, can be written as :
That's a general equation of plane where is the normal vector
OK so if the equation of a plane is ax + by + cz = d you can just read off that the normal vector is (a,b,c)... but why is this? Is there a geometric kind of argument for why it's like that, or is it just a handy co-incidence?