Equation of the curve in space?

The equation of a curve in space is typically represented parametrically as ( \textbf{r}(t) = (x(t), y(t), z(t)) ), where ( t ) is a parameter that varies along the curve and determines the position of points on the curve. Each component function ( x(t), y(t), z(t) ) defines the coordinate values of points on the curve at different values of ( t ).