We describe completely the so called jet like functors of a vector bundle $E$ over an $m$-dimensional manifold $M$, i.e. bundles $FE$ over $M$ canonically depending on $E$ such that $F(E_1\times_M E_2)=FE_1\times_MFE_2$ for any vector bundles $E_1$ and $E_2$ over $M$. Then we study how a linear vector field on $E$ can induce canonically a vector field on $FE$.