What is a Vector? Definition and Examples

What is a vector? A vector, also called vector quantity, is a quantity that has both magnitude and direction. For example, suppose you are pulling a cart up a 25 degrees incline and it requires an effort of 75 pounds.

This situation is describing a vector because it has a magnitude and it has a direction. The magnitude is 75 pounds and the direction is 30 degrees from the horizontal. 

What is a vector geometrically?

Geometrically, a vector is a directed line segment with an initial point and a terminal point such as the one shown below.

We can use boldface letters such as v, w, s to denote vectors. Notice the boldface letter v used above to denote the vector shown in blue.

Relationship between two vectors

There are four possible relationships between two vectors v and w


v = w because the vectors have the same magnitude and the same direction.

Equal vectors


v ≠ because the vectors have the same direction, but different magnitudes.

Vectors with different magnitudes.


v ≠ because the vectors have the same magnitudes, but different directions.

Vectors with different directions.


v ≠ because the vectors have the same magnitudes, but opposite directions.

Vectors with opposite directions.

More real life examples of vectors

  • Driving a car due south at 65 miles per hour.
  • Picking a box from the floor and lifting it straight up or at an angle.
  • Kicking a football with a speed of 38 feet per second at an angle of 50 degrees. 
Enjoy this page? Please pay it forward. Here's how...

Would you prefer to share this page with others by linking to it?

  1. Click on the HTML link code below.
  2. Copy and paste it, adding a note of your own, into your blog, a Web page, forums, a blog comment, your Facebook account, or anywhere that someone would find this page valuable.
Share this page: