Flashcards: Three Dimensional Geometry | Mathematics (Maths) for JEE Main & Advanced PDF Download

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THREE DIMENSIONAL GEOMETRY 
In the practical life different objects do not lie in same plane but in space. 
If we are to locate any object in universe three co-ordinates are required. 
Hence, three co-ordinates axes namely ?? ,?? &?? intersecting at that point, called origin are chosen in 
mutually perpendicular directions. In terms of 3 co-ordinates i.e. (?? ,?? ,?? ) any point in universe can be 
uniquely specified. 
  
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THREE DIMENSIONAL GEOMETRY 
In the practical life different objects do not lie in same plane but in space. 
If we are to locate any object in universe three co-ordinates are required. 
Hence, three co-ordinates axes namely ?? ,?? &?? intersecting at that point, called origin are chosen in 
mutually perpendicular directions. In terms of 3 co-ordinates i.e. (?? ,?? ,?? ) any point in universe can be 
uniquely specified. 
  
 
 
 
 
CO-ORDINATE AXES AND ORIGIN 
Let ???? ?? '
,???? ?? '
 and ???? ?? '
 are mutually perpendicular lines intersecting at ?? . ' ?? ' is called origin of co-
ordinate system. 
???? ? Positive direction of x-axis 
?? ?? '
? Negative direction of x-axis 
???? ? Positive direction of y-axis 
?? ?? '
? Negative direction of y-axis 
OZ ? Positive direction of z-axis 
?? ?? '
? Negative direction of z-axis 
  
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THREE DIMENSIONAL GEOMETRY 
In the practical life different objects do not lie in same plane but in space. 
If we are to locate any object in universe three co-ordinates are required. 
Hence, three co-ordinates axes namely ?? ,?? &?? intersecting at that point, called origin are chosen in 
mutually perpendicular directions. In terms of 3 co-ordinates i.e. (?? ,?? ,?? ) any point in universe can be 
uniquely specified. 
  
 
 
 
 
CO-ORDINATE AXES AND ORIGIN 
Let ???? ?? '
,???? ?? '
 and ???? ?? '
 are mutually perpendicular lines intersecting at ?? . ' ?? ' is called origin of co-
ordinate system. 
???? ? Positive direction of x-axis 
?? ?? '
? Negative direction of x-axis 
???? ? Positive direction of y-axis 
?? ?? '
? Negative direction of y-axis 
OZ ? Positive direction of z-axis 
?? ?? '
? Negative direction of z-axis 
  
 
 
 
CO-ORDINATE AXES AND ORIGIN 
 
  
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THREE DIMENSIONAL GEOMETRY 
In the practical life different objects do not lie in same plane but in space. 
If we are to locate any object in universe three co-ordinates are required. 
Hence, three co-ordinates axes namely ?? ,?? &?? intersecting at that point, called origin are chosen in 
mutually perpendicular directions. In terms of 3 co-ordinates i.e. (?? ,?? ,?? ) any point in universe can be 
uniquely specified. 
  
 
 
 
 
CO-ORDINATE AXES AND ORIGIN 
Let ???? ?? '
,???? ?? '
 and ???? ?? '
 are mutually perpendicular lines intersecting at ?? . ' ?? ' is called origin of co-
ordinate system. 
???? ? Positive direction of x-axis 
?? ?? '
? Negative direction of x-axis 
???? ? Positive direction of y-axis 
?? ?? '
? Negative direction of y-axis 
OZ ? Positive direction of z-axis 
?? ?? '
? Negative direction of z-axis 
  
 
 
 
CO-ORDINATE AXES AND ORIGIN 
 
  
 
 
 
 
COORDINATE PLANES 
?????? is called xy-plane which is perpendicular to Z-axis. ?????? is called yz-plane which is perpendicular to 
X-axis. ?????? is called zx-plane which is perpendicular to Y-axis. these three planes divide the space into 8 
octants, namely ???????? , ?? '
?????? ,?????? ?? '
,???? ?? '
?? ,?? '
???? ?? '
,???? ?? '
?? '
,?? '
?? ?? '
?? '
&?? '
?? ?? '
?? . 
  
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THREE DIMENSIONAL GEOMETRY 
In the practical life different objects do not lie in same plane but in space. 
If we are to locate any object in universe three co-ordinates are required. 
Hence, three co-ordinates axes namely ?? ,?? &?? intersecting at that point, called origin are chosen in 
mutually perpendicular directions. In terms of 3 co-ordinates i.e. (?? ,?? ,?? ) any point in universe can be 
uniquely specified. 
  
 
 
 
 
CO-ORDINATE AXES AND ORIGIN 
Let ???? ?? '
,???? ?? '
 and ???? ?? '
 are mutually perpendicular lines intersecting at ?? . ' ?? ' is called origin of co-
ordinate system. 
???? ? Positive direction of x-axis 
?? ?? '
? Negative direction of x-axis 
???? ? Positive direction of y-axis 
?? ?? '
? Negative direction of y-axis 
OZ ? Positive direction of z-axis 
?? ?? '
? Negative direction of z-axis 
  
 
 
 
CO-ORDINATE AXES AND ORIGIN 
 
  
 
 
 
 
COORDINATE PLANES 
?????? is called xy-plane which is perpendicular to Z-axis. ?????? is called yz-plane which is perpendicular to 
X-axis. ?????? is called zx-plane which is perpendicular to Y-axis. these three planes divide the space into 8 
octants, namely ???????? , ?? '
?????? ,?????? ?? '
,???? ?? '
?? ,?? '
???? ?? '
,???? ?? '
?? '
,?? '
?? ?? '
?? '
&?? '
?? ?? '
?? . 
  
 
 
 
COORDINATE PLANES