Flashcards: Three Dimensional Geometry

# 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.

Page 2

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

Page 3

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

Page 4

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 ???????? , ?? '
?????? ,?????? ?? '
,???? ?? '
?? ,?? '
???? ?? '
,???? ?? '
?? '
,?? '
?? ?? '
?? '
&?? '
?? ?? '
?? .

Page 5

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

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## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

## FAQs on Flashcards: Three Dimensional Geometry - Mathematics (Maths) for JEE Main & Advanced

 1. What are the basic concepts of three-dimensional geometry in the JEE exam?
Ans. Three-dimensional geometry in the JEE exam covers topics such as coordinates in space, distance formula, section formula, direction cosines, and direction ratios.
 2. How important is three-dimensional geometry in the JEE exam syllabus?
Ans. Three-dimensional geometry is an essential part of the JEE exam syllabus and is often tested in both the Mathematics and Physics sections of the exam.
 3. How can one effectively prepare for the three-dimensional geometry section in the JEE exam?
Ans. To prepare for the three-dimensional geometry section in the JEE exam, it is important to practice a variety of problems, understand the basic concepts thoroughly, and refer to study materials and previous year question papers.
 4. What are some common types of questions asked in the three-dimensional geometry section of the JEE exam?
Ans. Common types of questions in the three-dimensional geometry section of the JEE exam include finding the distance between two points in space, determining the coordinates of a point, and solving problems related to planes and lines in space.
 5. Are there any specific strategies to tackle three-dimensional geometry questions in the JEE exam effectively?
Ans. Some strategies to tackle three-dimensional geometry questions in the JEE exam effectively include visualizing the problem in space, breaking down complex problems into simpler steps, and practicing regularly to improve problem-solving skills.

## Mathematics (Maths) for JEE Main & Advanced

209 videos|443 docs|143 tests

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