Three-dimensional geometry Assignment Help

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Three-dimensional geometry:

RECTANGULAR COORDINATE SYSTEM IN SPACE

 

Let 'O' be any point in space and 455_Three-dimensional geometry2.png be three lines perpendicular to each other. These lines are called as coordinate axes and O is called origin. The planes XY, YZ, ZX are called as the coordinate planes.

 

     196_Three-dimensional geometry.png

Coordinates of a Point in Space:

Consider a point P in the space.  The position of point P can be given by triad (x, y, z) here x, y, z are perpendicular distance from YZ plane, ZX plane and XY plane respectively.

 

If We assume that 1250_Three-dimensional geometry4.png unit vectors along OX, OY, OZ respectively, then position vector of point P is 698_Three-dimensional geometry5.png or simply (x, y, z).

   2460_Three-dimensional geometry1.png

Note:

  • x-axis = {( x, y, z) | y = z = 0}
  • y-axis = {(x, y, z) | x = z = 0}
  • z-axis = {(x, y, z) | x = y = 0}
  • xy plane = {(x, y, z) | z = 0}
  • yz plane = {(x, y, z) | x = 0}
  • zx plane = {(x, y, z) | y = 0}
  • OP =  719_Three-dimensional geometry3.png

 

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