What are vector quantities and how do they work?
Many measurements can be described by using just one number. These are called SCALAR quantities. Examples are temperature, the wavelength of light in a laser beam, and one's weight or height. There are also other things that need both a direction described as well as the number that tells you how much of whatever you have. A simple example would be the movement of an airplane in flight. Not only do you need to know its speed (the scalar), but you also need to know its direction of flight (up, down, east, west, and so on). These are called VECTOR quantities. (For the airplane example, the vector that describes the direction and speed is called the VELOCITY vector.)
When you see vectors used in math or science books, they usually stick to 2 dimensional problems (i.e., the surface of the book page) for simplicity. Vectors are shown as a line segment with an arrow head at one end. In this way, the direction of the vector is obvious. The length of the line represents the amount of whatever (say, the speed of the airplane).
The neat thing about vectors is that one can also add them (as long as they represent the same thing) geometrically to find a new vector. For example, imagine a plane flying horizontally in a northerly direction at 500 miles per hour. However, there is also a wind blowing in a westerly direction at 100 miles per hour. By adding the velocity vectors for the plane and the wind, one can find the vector that properly describes the airplane's flight path (and speed).
You can find out more about SCALARS and VECTORS in the first couple of chapters in any high school physics book.
Carl Zorn, Detector Scientist (Other answers by Carl Zorn)