  The vector form of a Lorentz transformation which is separated with time and
space parts is studied. It is necessary to introduce a new definition of the
relative velocity in this transformation, which plays an important role for the
calculations of various invariant physical quantities. The Lorentz
transformation expressed with this vector form is geometrically well
interpreted in a hyperbolic space. It is shown that the Lorentz transformation
can be interpreted as the law of cosines and sines for a hyperbolic triangle in
hyperbolic trigonometry. So the triangle made by the two origins of inertial
frames and a moving particle has the angles whose sum is less than $180 ^o$.
