Page 1
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
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(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
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?
?
?
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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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