# Vector Quantity in Physics: Definition, Examples & Quiz

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### Richard Cardenas

Richard Cardenas has taught Physics for 15 years. He has a Ph.D. in Physics with a focus on Biological Physics.

A vector refers to any quantity that needs a magnitude and a direction in order to fully describe the quantity. In this lesson you will learn about the properties of vectors (magnitude and direction) and how to determine what quantities are vectors and what are not vectors.

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## Definition of a Vector Quantity

When someone tells you to throw a ball twice as hard and to the left, a vector was just used. When someone tells you to drive north east for about 5 miles, a vector was just used. So what exactly is a vector? Any quantity that needs to be fully described by identifying its magnitude and direction is referred to as a vector quantity. By magnitude we mean size of the quantity, such as length or strength. By direction we mean where the vector is pointing or where it is being directed, such as left or right, North, South, East, or West, or even up or down.

## How a Vector Is Represented

When a vector is drawn, it is represented by an arrow whose length represents the vector's magnitude, and whose arrow head points in the direction of the vector as shown in the figure below.

If the vector represents a quantity in one dimension (x-direction or left and right, or y-direction or up and down), then a vector will be written as a number with a plus (+) or minus (-) sign in front of it. The plus refers to pointing right or up and the minus refers to pointing left or down. In two dimensions (x and y), a vector will be represented with a number (for magnitude), and an angle (for direction).

## Examples of Vectors and Non-Vectors

When you use your global positioning system (GPS) in your car to help you get to your destination, the GPS unit will give you two pieces of information, such as drive 300 ft. then turn left. That is an example of a vector.

During a weather report, the reporter makes use of a vector when he states that at 1:00 a.m., the wind will blow north at 12 km/h and at 1:00 p.m. the wind is expected to blow eastward at 36 km/h. There is a magnitude (km/h) and a direction (North or East). In the picture below, the direction is represented by the arrow and the magnitude is represented by the speed listed below the arrow.

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