 We can also have parametric equations for curves in three or more dimensions, and nothing important changes in our analysis. The only thing that really changes is how we describe our results. For example, let's say a particle moves along a curve with the parametric equations, and let's describe the motion of the particle at t equals zero. So first, we find where we are. So our x-coordinate is, our y-coordinate is, and our z-coordinate is. And that tells us we're at the point one zero zero, and so we can find the derivatives at t equal to zero. So x-prime of zero is, which tells us that our x-coordinate is not changing. y-prime is, which tells us that the y-coordinate is increasing. And z-prime of zero is, which tells us that the z-coordinate is also increasing. Now we should be a little careful about how we're describing these directions. In two dimensions, we have a sense of right and up, but that's based on a particular point of view, and if we view from the first octant, we have to change how we speak of these directions. And so in this case, since y and z are both increasing, from the first octant viewpoint, the particle is moving right and upward.