Two vectors are considered orthogonal if \langle u,v \rangle = 0, that is, their inner product is 0. See also orthogonality test. orthogonality and 0 0 is orthogonal to every vector in v because \langle 0,v \rangle=0 for every v because of the properties of inner product 0 is the only vector orthogonal to itself as, by inner product definiteness, \langle v,v \rangle=0 implies v=0.