Another scalar quantity is speed. While traveling on a highway, your car’s speedometer may read “70
miles per hour.” It does not matter whether you are traveling north or south, if you are going forward or in
reverse: your speed is 70 miles per hour.
Vector Basics
Vectors, by comparison, have both magnitude and direction.
Direction: The orientation of a vectorAn example of a vector is velocity. Velocity, unlike speed, always has a direction. So, let’s say you are
traveling on the highway again at a speed of 70 miles per hour. First, define what direction is positive—
we’ll call north the positive direction. So, if you are going north, your velocity is +70 miles per hour. The
magnitude of your velocity is “70 miles per hour,” and the direction is “north.”
If you turn around and travel south, your velocity is −70 miles per hour. The magnitude (the speed) is
still the same, but the sign is reversed because you are traveling in the negative direction. The direction of
your velocity is “south.”
IMPORTANT: If the answer to a free-response question is a vector quantity, be sure to state both the
magnitude and direction. However, don’t use a negative sign if you can help it! Rather than “−70 miles
per hour,” state the true meaning of the negative sign: “70 miles per hour, south.”
Graphic Representation of Vectors
Vectors are drawn as arrows. The length of the arrow corresponds to the magnitude of the vector—the
longer the arrow, the greater the magnitude of the vector. The direction in which the arrow points
represents the direction of the vector. Figure 9.1 shows a few examples:
Figure 9.1 Examples of vectors.