Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Rectangle Cartesian coordinates in space

\to \overleftrightarrow{xx'},\overleftrightarrow{yy'} \text { and }\overleftrightarrow{zz'} are mutually perpendicular line in space. (x,y,z -axes)

\to x,y \text { z}-axes are called coordinate axes.

\to O is called origin. The coordinate of  O is (0, 0, 0) .

\toThe planes containing the pairs of intersecting lines  (\overleftrightarrow{x'x},\quad \overleftrightarrow{y'y}),\quad(\overleftrightarrow{y'y}, \quad\overleftrightarrow{z'z}) \text { and } (\overleftrightarrow{z'z},\quad \overleftrightarrow{x'x}) are called coordinate planes named respectively as xy, yz, \text { and } zx -planes.

\toThe  x,y \text { and } z-axes are respectively perpendicular to  yz, zx \text { and } xy-planes. The system of axes thus obtained is known as rectangular or orthogonal system of coordinate axes.

Note:

\to  \overrightarrow{ox},\overrightarrow{oy} \text { and }\overrightarrow{oz} are called the non-negative  x, y \text { and } z-axes and \overrightarrow{ox'},\overrightarrow{oy'} \text { and }\overrightarrow{oz'} are non-positive  x, y \text { and } z-axes respectively.

\to The above system of coordinates is known as the Rectangular Cartesian Coordinate System, named after the French mathematician Rene Descartes (1596-1650).

The octants:

 

The three coordinate planes, (xy, yz  \text{ and } zx- planes) intersecting at origin divide the set of points not living on any of the coordinate planes into eight disjoint convex sets known as Octants.

A three dimensional space with  R^{3} , we can describe the eight octants as follows:

  1. oxyz=\{(x,y,z) \in R^3 |x>0, y>0,z > 0\}
  2.  ox'yz=\{(x,y,z) \in R^3 |x<0, y> 0,z > 0\}
  3.  ox'y'z=\{(x,y,z) \in R^3 |x<0, y < 0,z > 0\}
  4.  oxy'z=\{(x,y,z) \in R^3 |x > 0, y < 0,z > 0\}
  5. oxyz'=\{(x,y,z) \in R^3 |x > 0, y > 0,z < 0\}
  6. ox'yz'=\{(x,y,z) \in R^3 |x < 0, y > 0,z < 0\}
  7.  ox'y'z'=\{(x,y,z) \in R^3 |x < 0, y < 0,z < 0\}
  8. oxy'z'=\{(x,y,z) \in R^3 |x > 0, y < 0,z < 0\}

 

 

 

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