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6: Vectors

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    In this chapter, we will look at vectors in several forms. Once we have a general understanding of notation, we will learn how vectors have a wide range of applications in surveying, work, force and tension. We may also find how helpful these vectors can be for manipulating free-body diagrams (used widely in physics).

    • 6.0: Prelude to Vectors
      In this chapter, we will investigate matrices and their inverses, and various ways to use matrices to solve systems of equations. First, however, we will study systems of equations on their own: linear and nonlinear, and then partial fractions. We will not be breaking any secret codes here, but we will lay the foundation for future courses.
    • 6.1: Vectors from a Geometric Point of View
      There are some quantities that require only a number to describe them. We call this number the magnitude of the quantity. One such example is temperature since we describe this with only a number such as 68 degrees Fahrenheit. Other such quantities are length, area, and mass. These types of quantities are often called scalar quantities. However, there are other quantities that require both a magnitude and a direction. One such example is force, and another is velocity.
    • 6.2: Vectors from an Algebraic Point of View
      We have seen that a vector is completely determined by magnitude and direction. So two vectors that have the same magnitude and direction are equal. That means that we can position our vector in the plane and identify it in different ways.  Vectors also have certain geometric properties such as length and a direction angle. With the use of the component form of a vector, we can write algebraic formulas for these properties.
    • 6.3: Solving Systems of Equations with Augmented Matrices
      This is a short introduction to using an augmented matrix to solve a system of equations using a calculator instead of substitution or elimination by hand.
    • 6.E: Triangles and Vectors (Exercises)

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