A vector quantity is defined as a quantity that has both magnitude and direction. vector quantities, one must know the method for representing these quantities.

To work with

Magnitude, or "size" of a vector, is also referred to as the vector's "displacement." It can be thought of as the scalar portion of the vector and is represented by the length of the vector. By definition, a vector has both magnitude and direction. Direction indicates how the vector is oriented relative to some reference axis, as shown in Figure 1.

Using north/south and east/west reference axes, vector "A" is oriented in the NE quadrant with a direction of 45 north of the EW axis. G iving direction to scalar "A" makes it a vector. The length of "A" is representative of its magnitude or displacement.

Figure I Vector Reference Axis

To help distinguish between a scalar and a vector, let's look at an example where the only information known is that a car is moving at 50 miles per hour. The information given (50 mph) only refers to the car's speed, which is a scalar quantity. It does not indicate the direction the car is moving. However, the same car traveling at 50 mph due east indicates the velocity of the car because it has magnitude (50 mph) and direction (due east); therefore, a vector is indicated. When a vector is diagrammed, a straight line is drawn to show the unit of length. An arrow is drawn on one end of the line. The length of the line represents the magnitude of the vector, and the arrow represents the direction of the vector.

Description of a Simple Vector

Vectors are simple straight lines used to illustrate the direction and magnitude of certain quantities. Vectors have a starting point at one end (tail) and an arrow at the opposite end (head), as shown in Figure 2.

Figure 2 Vector

Examples of Vector Quantities

Displacement, velocity, acceleration, and force are examples of vector quantities. Momentum and magnetic field strength are also good examples of vector quantities, although somewhat more difficult to understand. In each of these examples, the main ingredients of magnitude and direction are present.