Three Dimensional Geometry
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 .
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
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
On solving (ii) and (iii) by cross multiplication, we get
Putting these values in (i), we get
which is the required equation of the plane.