What Is a Vector? - Definition & Types

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  • 0:25 What Is A Vector?
  • 1:58 Examples Of Vectors
  • 3:00 Manipulating Vectors
  • 4:01 Lesson Summary
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you will be able to explain what vectors are in physics, give some examples of vectors and have a basic idea of how they can be manipulated mathematically. A short quiz will follow.

What is a Vector?

One day, you go a little bit crazy and run around your home, in and out of every piece of furniture until you're dizzy and collapse onto the sofa. In the process, you ran a total of 400 meters. Not too shabby. But if you started on the sofa and ended on the sofa, then your displacement was zero. If you finish where you started, you didn't really go anywhere, and that's because the physics quantity of displacement is a vector.

A vector is a quantity that has both magnitude (numerical size) and direction. This is the opposite of a scalar, which is a quantity that only has magnitude and no direction.

So for example, a car might be going at 60 miles per hour. That's the car's speed, which is a scalar quantity. But the car's velocity might be 60 miles per hour north - for it to be a velocity, it has to have a direction. So when a baseball commentator compliments a pitcher's velocity, unless he's also talking about the pitcher's placement, he almost certainly doesn't know what the word means.

Distance is a scalar quantity that tells you how far you ran around the house - that's your 400 meters. Since it's a scalar, the direction you ran is irrelevant. The only thing that matters is how far you traveled. But displacement is a vector quantity and measures the difference in your position from where you started to where you ended, and if you finish up in the same place you started, your displacement is zero. The direction or directions you ran does have an impact on your displacement because displacement is a vector.

Vectors are represented diagrammatically with an arrow. A long arrow represents a big number, and a small arrow represents a small number. The direction of the arrow represents. . . the, er, direction.

Examples of Vectors

There are many examples of vector quantities in physics. We've already mentioned displacement and velocity. But acceleration is also a vector. Force is a vector, since when you push on something, you always push in a particular direction.

So, you have pushing force vectors but also gravitational force vectors, electric force vectors and magnetic force vectors. Fields are also vectors: you can have a vector for gravitational field strength, electric field strength and magnetic field strength, too. But those are all fairly abstract concepts. What about in everyday life?

Although there are considerably less overt examples of vectors in most people's life experiences, there are a couple. For example, if you've ever seen a traditional wind-speed map on a weather report, the ones with lots of arrows of different sizes, those are examples of vectors too. The arrows are larger to indicate a stronger wind, and the direction of the arrow shows you where the wind is pointed. So a wind-speed map is a map of vectors.

Manipulating Vectors

There are advantages to representing a quantity as a vector, and those advantages lie in how you can manipulate them.

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