Vectors in Math: Addition, Subtraction, Division & Multiplication

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Circles: Area and Circumference

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:01 Quick Review of Vectors
  • 1:03 Adding Vectors
  • 2:06 Subtracting Vectors
  • 2:31 Multiplying Vectors
  • 3:10 Dividing Vectors
  • 3:47 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Login or Sign up

Timeline
Autoplay
Autoplay
Create an account to start this course today
Try it free for 5 days!
Create An Account

Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

From airplanes to walking in a straight line, vectors are everywhere. In this lesson, we're going to learn how to add, subtract, multiply, and divide vectors helping us make more sense of them.

Quick Review of Vectors

Have you ever been on a plane and wondered what the pilot meant when she mentioned a headwind or a tailwind? Why in the world would such things matter to your arrival time? Or have you ever looked up on a windy day and swore that the birds were actually flying sideways? No, I'm afraid you didn't bump your head. Instead, what you are seeing is the world of vectors at work.

Remember that a vector is a magnitude combined with a direction. Saying we went north does not qualify as a vector. However, saying we walked two miles per hour north does. When graphed, vectors show their magnitude, or overall strength of force, by how long they are. This could often just be the number of miles traveled within a given time frame, often an hour. The direction of a vector is indicated by the direction of the line. In this lesson, we're going to learn how to add, subtract, and multiply vectors.

Adding Vectors

First things first, relax! Yes, you're going to have vectors going in odd angles from each other, but that doesn't mean that you'll have to learn any advanced trigonometry. In fact, you won't need any trigonometry at all to add vectors. Simply start at the tail of one of the vectors and draw a line to the tip of the other. Since vectors show their magnitude over a given time, this new line represents how the object in question will actually move over the course of that given time.

Say you had a vector with a magnitude of ten going northeast and a vector with a magnitude of four going north. First things first, draw the first vector. It doesn't matter which you choose. Now, at the tip of that vector, draw the tail of the second one. Draw out the vector like you would anywhere else. Now, simply draw a line from the tail of the first vector to the tip of the second vector. That is the result of adding these two vectors! Oddly enough, the resulting vector is called the resultant.

Subtracting Vectors

In order to subtract vectors, you do basically the same thing but with one minor adjustment. Instead of drawing the second vector as is, flip it 180 degrees so that it has completely changed direction. In effect, you are adding a negative quantity to the first vector, so it would go in the opposite direction than what is listed. From there, simply carry out the addition of vectors like before.

To unlock this lesson you must be a Study.com Member.
Create your account

Register for a free trial

Are you a student or a teacher?
I am a teacher

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it free for 5 days!
Create An Account
Support