What's a time-dependent vector field?

Question

Question might seem silly, but I can't put it together. Suppose we got a vector field $V: \textbf{x}\in U \subset \mathbb{R}^n \to \mathbb{R}^n$ so for instance for 3 Dimensions any point $(x,y,z)$ is pointing to another point $V(\textbf{x}) = \left(\begin{array}{c} v_1(x,y,z) \\v_2(x,y,z) \\ v_3(x,y,z) \end{array}\right)$ forming a vector. Now a time-dependent vector field is defined as $(t,x) \to V_t(\textbf{x})$. How's it looking? $V_t(\textbf{x}) = \left(\begin{array}{c} v_1(x,y,z,t) \\v_2(x,y,z,t) \\ v_3(x,y,z,t) \end{array}\right)$ ? The point to that a point $(x,y,z)$ is pointing to is changing in time?