Parametrizing Curves

A curve in 3D can be defined parametrically by:

$$C:x=x(t),y=y(t),z=z(t),\alpha \le t\le \beta$$

Equivalently, this can be represented as a vector function:

$$C:r(t)=⟨x(t),y(t),z(t)⟩,\alpha \le t\le \beta$$