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Introduction to Three Dimensional Geometry Class 11 Notes Maths

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KEY POINTS
? Three mutually perpendicular lines in space define three 
mutually perpendicular planes, called Coordinate planes, which 
in turn divide the space into eight parts known as octants and 
the lines are known as Coordinate axes. 
Coordinate axes: XOX', YOY', ZOZ' 
Coordinate planes: XOY, YOZ, ZOX or 
XY, YX, ZX planes 
Y Y´ 
Z 
Z´ 
X 
X´ 
O 
Page 2


 
KEY POINTS
? Three mutually perpendicular lines in space define three 
mutually perpendicular planes, called Coordinate planes, which 
in turn divide the space into eight parts known as octants and 
the lines are known as Coordinate axes. 
Coordinate axes: XOX', YOY', ZOZ' 
Coordinate planes: XOY, YOZ, ZOX or 
XY, YX, ZX planes 
Y Y´ 
Z 
Z´ 
X 
X´ 
O 
 
Octants: OXYZ, OX'YZ, OXY'Z, OXYZ' 
OX' Y'Z, OXY'Z', OX'YZ', OX'Y'Z' 
? Coordinates of a points lying on x-axis, y-axis & z-axis are of the 
from (x,0,0), (0,y,0),(0,0,z) respectively. 
? Coordinates of a points lying on xy-plane, yz-plane, & xz- plane 
are of the from (x,y,0), (0,y,z),(x,0,z) respectively. 
? The reflection of the point (x, y, z) in xy-plane yz-plane, &xz- 
plane is  (x,y,–z), (–x,y,z),(x,–y,z) respectively. 
? Coordinates of a point P are the perpendicular distances of P 
from three coordinate planes YZ, ZX and XY respectively. 
\
? The distance between the point A(x1, y1, z1) and B(x2, y2, z2) 
is given by 
Page 3


 
KEY POINTS
? Three mutually perpendicular lines in space define three 
mutually perpendicular planes, called Coordinate planes, which 
in turn divide the space into eight parts known as octants and 
the lines are known as Coordinate axes. 
Coordinate axes: XOX', YOY', ZOZ' 
Coordinate planes: XOY, YOZ, ZOX or 
XY, YX, ZX planes 
Y Y´ 
Z 
Z´ 
X 
X´ 
O 
 
Octants: OXYZ, OX'YZ, OXY'Z, OXYZ' 
OX' Y'Z, OXY'Z', OX'YZ', OX'Y'Z' 
? Coordinates of a points lying on x-axis, y-axis & z-axis are of the 
from (x,0,0), (0,y,0),(0,0,z) respectively. 
? Coordinates of a points lying on xy-plane, yz-plane, & xz- plane 
are of the from (x,y,0), (0,y,z),(x,0,z) respectively. 
? The reflection of the point (x, y, z) in xy-plane yz-plane, &xz- 
plane is  (x,y,–z), (–x,y,z),(x,–y,z) respectively. 
? Coordinates of a point P are the perpendicular distances of P 
from three coordinate planes YZ, ZX and XY respectively. 
\
? The distance between the point A(x1, y1, z1) and B(x2, y2, z2) 
is given by 
 
? Let P(x1, y1, z1) and Q (x2, y2, z2) be two points in space and 
let R be a point on line segment PQ such that it divides PQ in 
the ratio m1 : m2 
(I) internally, then the coordinates of R are 
1 2 2 1 1 2 2 1 1 2 2 1
1 2 1 2 1 2
m x m x m y m y m z m z
, ,
m m m m m m
? ?
? ? ?
? ?
?
?
?
? ?
? ? ? ? ?
 
(II) externally, then coordinates of R are 
1 2 2 1 1 2 2 1 1 2 2 1
1 2 1 2 1 2
m x m x m y m y m z m z
, ,
m m m m m m
? ?
? ? ?
? ?
?
?
?
? ?
? ? ? ? ?
 
Coordinates of centroid of a triangle whose vertices are 
1 1 1 2 2 2
(x , y , z ),(x , y , z ) and 
3 3 3
(x , y , z ) are 
3 3 3 1 1 1 2 2 2
x y z x y z x y z
, ,
3 3 3
? ?
? ? ? ? ? ?
? ?
?
?
?
? ?
? ?
 
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