Analyze the following statements regarding the fundamental properties of vectors in a plane.
I. A vector remains unchanged if it is displaced parallel to itself.
II. The magnitude of the sum of two vectors is always greater than the magnitude of their difference.
III. If the dot product of two non-zero vectors is zero, the vectors are perpendicular to each other.
IV. Vector addition is commutative, meaning A + B = B + A.
V. The division of a vector by a scalar is not defined.
