Introduction to Three Dimensional Geometry Video Lecture | Mathematics for Grade 11

in this module you will learn about the
coordinates of a point in space
we have seen how to locate a point in a
two dimensional plane with respect to
its distance from the reference axis
in three-dimensional space we identify a
point with respect to the distances from
the three reference planes
let's see what these reference planes
are and how to locate a point in space
we take two planes perpendicular to each
other the intersection of these two
perpendicular planes is a straight line
let's take another plane perpendicular
to both the existing planes with the
intersection of this plane with the two
existing planes
we get three lines mutually
perpendicular to each other these lines
are called
axes and are named as X Y and Zed
point of their concurrence is called the
origin
the origin is denoted by the letter O by
convention
the XY plane as the horizontal plane
distances are measured starting from the
origin distance is measured in one
direction are taken as positive
and in the opposite side as negative
for example
the distance measured from the origin
along the x-axis along the direction
shown is taken as positive
the distance measured from the origin in
the opposite side is considered negative
to indicate this we assign the symbol X
- a similar convention is followed for
calculating the distances along the y
and z axes
the plane formed by the x and y-axes is
called the XY plane
similarly
the plane formed by the y and z-axes is
called the Y Z plane
and the plane formed by the Z and X axis
is called the ZX plane
the xy-plane
y'see plane and ZX plane divide space
into eight octants
you
here X or Y Z is an octant this octant
is enclosed by the XYZ axes similarly
octants are named according to the axes
that enclose them
any point in space is represented with
the help of the distances that it
measures with respect to the planes
these distances are called the
coordinates of the point suppose we have
a point P in space the coordinates of
this point are X comma Y comma Z
each coordinate individually indicates
the shortest distance of the point from
the corresponding plane
for example
the coordinate X determines the shortest
distance of the point from the Y Z plane
similarly
the y-coordinate represents the distance
of the point from the Z explained
and Zen represents the distance of the
point from the XY plane
ordinance of the origin are zero comma
zero comma zero
having seen the coordinate axes we will
explore how we use the coordinate axes
in locating a point in the coordinate
space
given a point in space
we can measure its distance from the
coordinate planes let's see how
one way is to drop a perpendicular on
the XY plane
let this perpendicular meet the xy-plane
at Point Q
then we drop a perpendicular from Q on
the x-axis
this meets at a point say odd
distance pod is the x-coordinate
RQ is the y-coordinate and pink.you
is the Z coordinate
if we are given the coordinates of a
point then we can trace the point as
shown
we will identify a point CR
the x-axes which is at a distance X from
the origin
next
we draw a perpendicular of length Y from
point R and parallel to the y-axis on
the XY plane to a point say Q lastly we
draw a perpendicular of length Z from
point Q perpendicular to the XY plane we
can observe an interesting property
among the coordinates of the points any
point that lies on the x axis will have
its coordinates in the form X comma 0
comma 0
for example
a point at a distance of six units from
the origin
on the x-axis we'll have the coordinates
six comma zero comma zero
similarly the points that lie on y-axis
will have coordinates of the form 0
comma y comma 0
and the points on the z-axis will have
coordinates of the form zero comma zero
commas end
you're the letters X Y & Z belong to the
set of real numbers
any point on the XY plane will be of the
form
X comma y comma 0
shown here are some points on the XY
plane
any point on the Y Z plane will be of
the form
zero comma y comma Z and a point on the
Z X plane will be of the form X comma
zero comma Z
you're the letters X Y & Z belong to the
set of real numbers
having seen how a given point is traced
in space
we will now locate a point using the
intersection of planes
first we will take a plane at a distance
X and parallel to the Y Z plane next a
plane parallel to the XZ plane and at a
distance of Y is taken finally
another plane parallel to the XY plane
and at a distance of Z is taken first
let's take two planes one parallel to
the Y Z plane and the other parallel to
the XZ plane
the intersection will be aligned
parallel to the z-axis likewise
the intersection of the other planes
creates lines as shown
concurrence of these lines is point P
the coordinate axes divide the
coordinate space into eight parts called
octants
the sign of the continents determine the
position of a point in a particular
octant
for example the point two comma minus
three comma three lies in the fourth
octant
the x-coordinate of the point is too
so we measure two units along the x axis
and marker point the y coordinate is
minus three so from this point
we measure three units on the XY plane
in the direction of oh why - parallel to
the y axes
we mark a point there
for the z-coordinate that is three we
measure three units from the point
perpendicular to the XY plane
we can notice that the point lies in the
fourth octant
the table shown here gives the details
of the octant according to the signs of
the coordinates of a given point
in this module you learned that the
coordinate space together with
coordinate axes
is called the coordinate system
the coordinate axes divide the
coordinates space into eight parts
called octants
any point that lies on the x-axis will
have its coordinates in the bomb
X comma zero comma zero
any point that lies on the y-axis will
have its coordinates in the form 0 comma
y comma 0
any point that lies on the z-axis will
have its coordinates in the form zero
comma zero commas end
any point on the XY plane will be of the
form X comma Y comma 0
any point on the Y Z plane will be of
the form 0 comma y comma Z
any point on the ZX plane will be of the
form X comma zero commas end