The following mathlet allows you to visualize the motion of some parametric equations in 3D.

• The top left drop-down allows you to choose from several different parametric equations.
• The center view shows the $x$-$y$-$z$-axes, the particle's trajectory, and the particle's position at a given time $t$. There are also options to display the unit tangent vector or velocity vector (scaled to fit).
• At the bottom is a slider for the value of $t$.

Notice that the velocity vector points tangent to the particle's trajectory. Take note of the difference between the unit tangent vector and the velocity vector.