Show that the equation ax+by+d=0 represents a plane parallel to th | Filo
filo Logodropdown-logo

Class 12

Math

3D Geometry

Three Dimensional Geometry

view icon558
like icon150

Show that the equation represents a plane parallel to the z-axis. Hence, find the equation of a plane which is parallel to the z-axis and passes through the points and .

Solution:
The given equation is which is of the form .
Therefore, it represents a plane.
Direction ratio of normal to the plane are
Direction ratio of the z-axis are

Now,
This shows that the given plane is parallel to the z-axis.

Let the required plane be ..........(i)
Since it passes through the points and , we have
........(ii)
.........(iii)
On solving (ii) and (iii) by cross multiplication, we get
(say)
and

Putting these values in (i), we get
,
which is the required equation of the plane.
view icon558
like icon150
filo banner image

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

playstore logoplaystore logo
Similar Topics
three dimensional geometry
different products of vectors and their geometrical applications
three-dimensional geometry
vector algebra
conic sections