define equallity of two vectors

Dear Ankush

Two vectors are said to be equal if they have the same magnitude and direction. In the figure below, three equal vectors have been represented. The equality of vectors is expressed in the following way

Since the three vectors have the same direction,

Moreover, the three vectors are also equal in magnitude.

If the scales selected for the representation of three vectors are the same, then, three equal vectors are represented by three arrows of equal lengths, pointing in the same direction. If, however, the scales chosen are different, then, it is possible to represent equal vectors by arrows of different lengths. Equality of two vectors does not depend upon their location in space. A direct consequence of this physical fact is that a vector can be displaced parallel to itself. This fact may be used in testing the equality of two vectors. It would be of interest to note that, to compare two vectors with different physical dimensions, would be absolutely meaningless. For example, it is not possible to compare a velocity vector with a force vector.

All the best.                                                           

AKASH GOYAL

AskiitiansExpert-IIT Delhi

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