Two vectors are defined to be equal if they have the same magnitude and the same dirction. Graphically, this means that they have the same length and are parallel to each other.A consequence of the definition is that moving vector so that it remains parallel to itself does not change it. Vectors do not depend on the coordinate system used to represent them. In comparing vectors and performing other mathematical operations such as addition and subtraction, we may translate vectors anywhere in the coordinate space for convenience. We must be careful,however, to preserve their magnitude and directions with respect to axes.