Planes

Which of the following statements are true?

I: For every plane, there is an infinite number of equations in the form $ax + by + cz + d = 0$ to represent the same plane but in all of these equations, $a, b, c, d$ all remain in the same proportions to each other.

II: For every plane, there is an infinite number of equations in the form $\vec{n} \cdot (\vec{v} - \vec{v_0}) = 0$ to represent the same plane, where $\vec{n}$ is the normal vector to the plane and $\vec{v} - \vec{v_0}$ is a vector in the plane.

III: The same plane can have multiple equations, but only by the method of changing the norm (magnitude/length/absolute value) of the normal vector to the plane.