So according to this, the signed distance between a point and a plane will be the dot product of the plane's normal vector (does it have to be a unit vector?) and the point-in-plane minus the point vector.
I searched everywhere and I can't find a good explanation on why does the dot product give the correct answer. I even studied a little bit more about the dot product itself and I came to know that the dot product of a * b is like multiplying the magnitudes of the vectors that go on the same direction. This still doesn't help me understand my problem.
If it matters, I encountered this problem as a programmer.