Vectors in the plane and space

  • Larry Smith
Part of the Undergraduate Texts in Mathematics book series (UTM)


In physics certain quantities such as force, displacement, velocity, and acceleration possess both a magnitude and a direction and they are most usually represented geometrically by drawing an arrow with the magnitude and direction of the quantity in question. Physicists refer to the arrow as a vector, and call the quantities so represented vector quantities. In the study of the calculus the student has no doubt encountered vectors, and their algebra, particularly in connection with the study of lines and planes and the differential geometry of space curves. Vectors can be described as ordered pairs of points (P, Q) which we call the vector from P to Q and often denote by \(\overrightarrow {PQ}\). This is substantially the same as the physics definition, since all it amounts to is a technical description of the word “arrow.” P is called the initial point and Q the terminal point.


Initial Point Position Vector Line Passing Vector Equation Terminal Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag, New York Inc. 1978

Authors and Affiliations

  • Larry Smith
    • 1
    • 2
  1. 1.Mathematisches InstitutUniversität GöttingenGöttingenWest Germany
  2. 2.Department of MathematicsIndiana UniversityBloomingtonUSA

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