Show that the equation ax+by+d=0 represents a plane parallel to th | Filo
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Class 12


3D Geometry

Three Dimensional Geometry

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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.
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