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UExcel Physics: Study Guide & Test Prep17 chapters | 188 lessons

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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.

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.

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.

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

If your three children are pulling on your arms in three different directions, how do you know which child will win? Well, if you can represent those forces as vectors, all you need to do is add them tip-to-tail (graphically) or add the *x* and *y* components (mathematically). You can add or subtract vectors in this way to find the total; the resultant. The resultant vector is the overall force.

Or if you shoot a cannon at an angle of 60 degrees, you can represent that as a vector and use triangle geometry to break it up into a velocity in the *x*-direction and a velocity in the *y*-direction. That makes the motion of the cannonball much easier to understand.

We'll talk about each of these in more detail in other videos on vectors, but it's through these mathematical and graphical processes that vectors become extremely useful for understanding physical phenomena.

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.

Speed is a scalar: for example, 60 miles per hour. Velocity is a vector: 60 miles per hour north. Distance is a scalar: four miles total. Displacement is a vector: two miles away from your starting position. Any quantity where the direction matters is a vector quantity.

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 direction.

Example of vectors include displacement, velocity, acceleration, force and field strength. An everyday example of a vector would be an arrow on a wind-speed weather map.

Vectors allow you to do all kinds of mathematical manipulation, such as breaking a vector into *x* and *y* components or adding two vectors up to find a total. This makes them extremely useful for understanding physical phenomena.

After you have finished this lesson, you should be able to:

- Describe a vector and a scalar
- Recall examples of vectors
- Explain the use of vectors in mathematics

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UExcel Physics: Study Guide & Test Prep17 chapters | 188 lessons

- What Is a Vector? - Definition & Types 5:10
- Resultants of Vectors: Definition & Calculation 6:35
- Scalar Multiplication of Vectors: Definition & Calculations 6:27
- Vector Subtraction (Geometric): Formula & Examples 5:48
- Standard Basis Vectors: Definition & Examples 5:48
- How to Do Vector Operations Using Components 6:29
- Vector Components: The Magnitude of a Vector 3:55
- Vector Components: The Direction of a Vector 3:34
- Vector Resolution: Definition & Practice Problems 5:36
- Go to Vectors

- Go to Kinematics

- Go to Relativity

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