Graphing Vectors in Math: Magnitude & Direction

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  • 0:01 What is a Vector?
  • 1:06 What is Magnitude?
  • 1:39 Graphing Magnitude
  • 2:03 What is Direction?
  • 2:56 Graphing Direction
  • 3:28 Lesson Summary
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Lesson Transcript
Instructor: Kevin Newton

Kevin has edited encyclopedias, taught history, and has an MA in Islamic law/finance. He has since founded his own financial advice firm, Newton Analytical.

Vectors are some of the most useful parts of math, but their usefulness is only apparent if you know how to graph them. In this lesson, we learn how to graph vectors with respect to both magnitude and direction.

What Is a Vector?

I know, I know, you've heard it time and time again that math is one of the most useful subjects that you'll learn. Sometimes it's hard to remember that when working with things like matrices and parabolas, but trust me, those have real uses. One topic in math that has a very obvious purpose is the study of vectors. When you were younger, you probably remember memorizing that a vector was a line that had exactly one defined end point. In that respect, it was like the combination of a line and a line segment.

However, admit it, that's not what you thought when you saw the title of this lesson. You were likely thinking this could have something to do with some lame sci-fi movie where they talk about finding the correct vector for docking. At least that's what I thought of when I decided to write this lesson! However, we're going to keep the science fiction to a minimum and focus on vectors in their most useful meaning - a quantity moving away from a defined point that has a defined direction and magnitude.

What Is Magnitude?

Ok, direction is pretty straightforward, and we'll discuss it more thoroughly in a moment. However, let's first talk about magnitude. Magnitude is the strength of a particular vector. Strength, however, can present in a number of different measures. It can be in terms of speed, force or any other measure of strength. The important thing is to remember that magnitude is a measure of just how much power that a particular vector has. When you start combining vectors together, the magnitude of a vector can change the course of many vectors with lesser magnitudes.

Graphing Magnitude

Luckily, graphing the vector of a magnitude is as easy as drawing a line. Typically when we graph a vector, we draw it for as long as its magnitude is. Therefore, if you were to look at two vectors on a graph, the one with the shorter length would be the one with the lesser magnitude. Likewise, the vector that stretches for the longest distance across the paper would be the vector that has the greatest magnitude.

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