
5. Find the vector equation of the following planes :
Solution.
Hence, the non-parametric form of the plane is
Solution.
So, the non-parametric form of the plane is
S N Dey mathematics class 12 solutions -Plane-Ex-5A
6. Find the vector equations of the plane passing through the points and
Solution.
Let the position vectors of three points lying on the plane be denoted by and
respectively.
So, lies on the plane .
Therefore, is normal vector to the plane.
So, the equation of the plane passing through and normal to
is
7. Find the equation of the plane passing through the following points :
and
Solution.
The equation of the plane which passes through three given points and
is
Using we get the required equation of the plane
and
Solution.
The required equation of the plane is given by
8. Show that the following points are coplanar :
and
Solution.
The equation of the plane passing through the points is given by
Now, the point lies on the plane
if the point satisfies the equation
So, putting on the L.H.S. of the equation
we get,
Clearly, the point satisfies the equation
and so the point lies on the plane.
Hence, the four points are coplanar.
and
Solution.
The equation of the plane containing three points is given by
Now, if lies on the plane
, the given point
must satisfy the equation
Putting on the L.H.S. of the equation
we get,
Clearly, the point satisfies the equation
and so the point lies on the plane.
Hence, the four points are coplanar.
9. Find the equation of the plane which makes equal (non zero) intercepts on the axes and passes through the point
Solution.
We know that the equation of the plane intercepts on the coordinate axes area and
is given by
Given that the plane makes equal intercepts on the co-ordinate axes and so,
the equation of the plane can be written as
Since the plane passes through the point
, we get from
Hence, the equation of the plane is