Given a vector p, in Cartesian space, there are unique real numbers x, y, and z such that p = xi + yj + zk, where i, j, and k are the canonical basis. Then xi, yj, and zk are the components of p with respect to i, j, k, and x, y, and z are the coordinates of p. These can be determined by using the scalar product: x = p∙i, y = p∙j and z = p∙k.

More generally, if u, v, and w are any 3 non-coplanar vectors, then any vector p in 3-dimensional space can be expressed uniquely as p = xu + yv + zw, and xu, yv, and zw are called the components of p with respect to the basis u, v, w, and x, y, and z are the coordinates of p with respect to u, v, w. In this case, however, the components cannot be found so simply by using the scalar product. See also vector projection.