  Besides the well known scalar invariants, there exist also vectorial
invariants in the realm of special relativity. It is shown that the
three-vector $\left(\frac{d\vec{p}}{dt}\right)_{\parallel
v}+\gamma_v\left(\frac{d\vec{p}}{dt}\right)_{\perp v}$ is invariant under the
Lorentz transformation. The indices $_{\parallel v}$ and $_{\perp v}$ denote
the respective components established with respect to the direction of the
velocity of body $\vec{v}$, and $\vec{p}$ is the relativistic momentum. We
prove that this vector is equal to a force of $\vec{F}_R$ satisfying the
classical Newtonian law $\vec{F}_R=m\vec{a}_R$ in the instantaneous inertial
rest frame of an accelerated body. Therefore the equation
$\vec{F}_R=\left(\frac{d\vec{p}}{dt}\right)_{\parallel
v}+\gamma_v\left(\frac{d\vec{p}}{dt}\right)_{\perp v}$, based on the
Lorentz-invariant vectors, may be used as a truly invariant (not merely a
covariant) relativistic equation of motion in any inertial system of reference.
An alternative approach to classical electrodynamics based on the invariant
three-vectors is proposed.
