unit vector

A unit vector is any vector whose magnitude equals exactly 1, carrying direction alone and no information about size. Dividing any nonzero vector by its own magnitude — a process called normalizing — produces the unit vector pointing the same way; the two special unit vectors \mathbf{i}=\langle 1,0\rangle and \mathbf{j}=\langle 0,1\rangle form the standard basis that every planar vector can be written in terms of.