## 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 northeast for about five 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 (left and right) or y-direction (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.