Many of the quantities and measurements we deal with in everyday life have not only a magnitude (a size like 2 or -5 or 0) but a direction as well - left, up, north, etc.. Quantities which have both a magnitude and a direction in 2-space or 3-space are called vector quantities, or vectors for short. Here are some examples of vector quantities.

Displacement. The displacement of a moving object is its final position relative to its starting position. If you leave from home, walk through the park, then to the supermarket and then to your friend's house 3 blocks north of your house, your displacement is 3 blocks north, no matter what route you took to get there.

 

Velocity. All traveling objects have a speed, but they also have a direction of travel. The combination of speed and travel direction is a vector quantity called velocity. Thus a car traveling 100 km/hour southwest has a different velocity than a car traveling 100 km/hour east, even though they have the same speed.

There are many other vector quantities. To distinguish vector quantities more clearly from quantities with only size, we call quantities with only magnitude scalar quantities, or scalars. So speed is a scalar quantity, for example, as is the total distance traveled by a moving object.

You already know how to calculate with scalars by adding them or multiplying them. In this learning object, you will look at

1. How to represent vectors geometrically
2. How to calculate with vectors geometrically, keeping track of the directions of your calculations as well as their magnitudes,
3. Some rules for vector calculations.

Force. Forces always have a direction associated with them.

• A rocket ship traveling straight up through the atmosphere experiences several forces: the force of gravity pulling it downward, the thrust of its rockets pushing it upward and the friction of the air pushing downward.
• A boat traveling up a river experiences a force from the water pushing it downstream and another from its engine pushing it upstream.