Lectures on Physics has been derived from Benjamin Crowell's Light and Matter series of free introductory textbooks on physics. See the editorial for more information....

For motion with constant velocity, the velocity vector is

v = Δr/Δt . [only for constant velocity]

The Δr vector points in the direction of the motion, and dividing
it by the scalar Δt only changes its length, not its direction, so the
velocity vector points in the same direction as the motion. When
the velocity is not constant, i.e., when the x-t, y-t, and z-t graphs
are not all linear, we use the slope-of-the-tangent-line approach to
define the components v_{x}, v_{y}, and v_{z}, from which we assemble the
velocity vector. Even when the velocity vector is not constant, it
still points along the direction of motion.
Vector addition is the correct way to generalize the one-dimensional
concept of adding velocities in relative motion, as shown in the following
example:

Velocity vectors in relative motion.

→ Solved problem: Annie Oakley page 217, problem 8

Discussion Questions

A

Is it possible for an airplane to maintain a constant velocity vector
but not a constant |v|? How about the opposite - a constant |v| but not a
constant velocity vector? Explain.

B

New York and Rome are at about the same latitude, so the earth's
rotation carries them both around nearly the same circle. Do the two cities
have the same velocity vector (relative to the center of the earth)? If not,
is there any way for two cities to have the same velocity vector?