‘Two‐arrowheaded’ or ‘senseless’ vectors are introduced as a new kind of entity in plane. By means of heuristic transformation W that duplicates the phases in the plane of ‘senseless’ vectors, they become ordinary vectors. In this way, the set of ‘senseless’ vectors in plane acquires the structure of an Euclidean vectorial space provided with adequate operations: addition, product by scalar and. scalar product. Uniaxial magnetic anisotropies are proposed as a physical example of these singular entities.