This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Section 13.1 ThreeDimensional Coordinate Systems Living in a 3dimensional World 1. ThreeDimensional Rectangular Coordinate System We can sketch the graph of a function of two variables in the plane: the xcoordinate is the input value and the y coordinate is the corre sponding output. To illustrate the graph of a function of two variables, we need two inputs and a single output  this means we need an extra dimension if we want to sketch a graph. We do this as following: (The right hand rule) With your right hand, point your thumb up, and your next finger and your middle finger outward per pendicular to each other. Draw three lines in the direction your thumb and fingers are pointing  label the line along your thumb the zaxis, your middle finger the yaxis and the re maining one the xaxis. The positive axis is in the direction your fingers point. z x y Any point P in 3 space is completely determined by its distance along the x , y and zaxis. In order to sketch a point P in 3 space, we associate the ordered triple ( a, b, c ) where P is a directed distance of a units in the xdirection, b units in the y direction, and c units in the zdirection. We will often denote a point P as P ( a, b, c ) or ( a, b, c ). We call the three axis the coordinate axis ....
View
Full
Document
This note was uploaded on 10/28/2010 for the course MA 261 taught by Professor Stefanov during the Fall '08 term at Purdue UniversityWest Lafayette.
 Fall '08
 Stefanov
 Calculus

Click to edit the document details