# Planes

Geometry Level pending

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.

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