#### Answer

A space curve is a curve in space. There is a close connection between space curves and vector functions.Specifically, we can determine a vector function which traces along a space curve $\bf{C}$( provided we put the tail of the vectors at the origin, so they are position vectors).
Likewise any function defines a space curve.
A vector-valued function, or a vector function, is a function whose domain is a set of real numbers and whose range $\bf{R}$ is a set of multidimensional vectors.Consider any vector function in form of $r(t)=f(t)i+g(t)j+h(t)k$
which we shall call a vector function of $\bf{C}$.
As $t$ varies, the position vector $r(t)$ traces out the curve $\bf{C}$.