x1 is the direction of vector x2 in Hilbert space (with basis/in coordinates, including defined scales and origins) x3; x1 is the direction of x2 in a Hilbert sense

For example: quantum spin vectors are in terms of Hilbert space directions (components are oriented along directionals that are oriented in a Hilbert sense, rather than a physical/spatial sense). Such directions are a subset of the set of all directions. See also: farna