Flow of a Vector Field

Question

If $V_r$ be a vector field defined on $S^2_r$ that is always tangent to the sphere on which it is defined.Define a vector field $V$ on $R^3$ such that $V(x)$=$r^2(1-r^2)$$V_r(x)$.Prove that for each $t \in R$ the time $t$ flow associated to this vector field is defined.