Engineering Calculus Notes 13

Engineering Calculus Notes 13 - rectangular or Cartesian...

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1 Coordinates and Vectors 1.1 Locating Points in Space Rectangular Coordinates The geometry of the number line R is quite straightforward: the location of a real number x relative to other numbers is determined—and speciFed—by the inequalities between it and other numbers x : if x < x then x is to the left of x , and if x > x then x is to the right of x . ±urthermore, the distance between x and x is just the di²erence x = x x ( resp . x x ) in the Frst ( resp . second) case, a situation summarized as the absolute value |△ x | = v v x x v v . When it comes to points in the plane, more subtle considerations are needed. The most familiar system for locating points in the plane is a
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Unformatted text preview: rectangular or Cartesian coordinate system . We pick a distinguished point called the origin and denoted O . Now we draw two axes through the origin: the Frst is called the x-axis and is by convention horizontal , while the second, or y-axis , is vertical . We regard each axis as a copy of the real line, with the origin corresponding to zero. Now, given a point P in the plane, we draw a rectangle with O and P as opposite vertices, and the two edges emanating 1...
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