A vector perpendicular to a given vector a is a vector a^⊥ (voiced "a-perp") such that a and a^⊥ form a right angle. In the plane, there are two vectors perpendicular to any given vector, one rotated 90° counterclockwise and the other rotated 90° clockwise. Hill defines a^⊥ to be the perpendicular vector obtained from an initial vector a = [a_x a_y] by a counterclockwise rotation by 90°, i.e., a^⊥ = [0 | -1 1 | 0] a = [-a_y a_x].

perp dot product | perpendicular | vector