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RD Sharma class 12th exercise 28.1 is a must-have NCERT solution for students in class 12. High school students in India have immense trust in RD Sharma Solutions. The RD Sharma class 12 solutions The Plane ex 28.1 will become an indispensable book for every student who takes their exam preparations seriously. The answers in the book can be incredibly helpful in checking students' performance and help them understand concepts better.
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The Plane exercise 28.1 question 1(i)
Answer:-
The required equation of the plane is
Hint:- Use equation of the plane and
Given:- and
Solution:- We know that, the equation of the plane passing through three non-collinear points and is
The Plane exercise 28.1 question 1(ii)
Answer:-
The required equation of the plane is
Hint:- Use equation of the plane and
Given:- and
Solution:- We know that, the equation of the plane passing through three non-collinear points and is
Now, substitute the given value
The Plane exercise 28.1 question 1(iii)
Answer:-
The required equation of plane is
Hint:- Use equation of the plane and
Given:- and
Solution:- We know that, the equation of the plane passing through given three points, and is
Now, substitute the given values
The Plane exercise 28.1 question 1(iv)
Answer:-
The required equation of the plane is
Hint:- Use equation of the plane and
Given:- and
Solution:- We know that, the equation of the plane passing through given three points, and is
Now, substitute the given value
The Plane exercise 28.1 question 1(v)
Answer:-
The required equation of the plane is
Hint:- Use equation of the plane and
Given:- and
Solution:- We know that, the equation of the plane passing through given three points, and is
Now, substitute the given value
The Plane exercise 28.1 question 2
Answer:-
The required equation of the plane is and hence they are coplanar.
Hint:- Use equation of the plane
Given:- and
Solution:- Given that these four points are coplanar. So these four points lie on the same plane.
So, first let us take three points and find the equation of the plane passing through these four points and then let us substitute the fourth point in it. If is 0 then the points lies on the plane formed by these three points then they are coplanar. The equation of the plane passing through these three points is given
Now, let us take and find plane equation
Now let us substitute fourth point we get
∴
So, as said above this fourth point satisfies. So, this point also lies on the same plane.
Hence they are coplanar.
Answer:-
Hence they are coplanar.
Hint:- Use the equation of plane
Given:- and
Solution:- Given that these four points are coplanar. So, these four points lie on the same plane.
So, first let us take three points and find the equation of plane passing through these four points and then let us substitute the fourth point in it. If it is 0 then the points lie on the plane formed by these three points then they are coplanar.
The equation of the plane passing through these three points is given
Now, let us take and find plane equation.
Now, let us substitute fourth point in plane equation
So, this point also lies on the plane.
Hence they are coplanar.
The Plane exercise 28.1 question 3(ii)
Answer:-
Hence they are coplanar.
Hint:- Use equation of plane
Given:- and
Solution:- Given that these four points are coplanar. So these four points lie on the same plane.
So, first let us take three points and find the equation of the plane passing through these four points and then let us substitute the fourth point in it. If it is 0 then the points lies on the plane formed by these three points then they are coplanar.
The equation of the plane passing through these three points is given by
Now, let us take and find plane equation
Now, let us substitute in plane equation
So, this point also lies on the plane.
Hence they are coplanar.
The Plane exercise 28.1 question 4
Answer:
Hence, externally divides the line segment in the ratio
Hint:
Use determinant then solve the equation of plane.
Given:
The equation of the plane three points
Solution:
The equation of the plane passing through three points can be given by:
Operating
Solving the above determinant, we get
Therefore, the equation of the plane is
Now, the equation of the line passing through two given points and is
At the point of intersection, these points satisfy the equation of the plane
Putting the value of and in the equation of the plane, we get the value of .
Thus, the point of intersection is .
Now,
Let divides the line in the ratio
By the section formula, we have
Here,
Hence, externally divides the line segment in the ratio .
RD Sharma class 12 solutions The Plane 28.1 is one book that will help students perfect their maths skills before board exams. The RD Sharma class 12th exercise 28.1 contains step-by-step solutions that are easy to understand and can also be understood by students who find maths difficult.
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The class 12 RD Sharma chapter 28 exercise 28.1 solution contains answers to the first exercise of the chapter. The questions in this exercise are on the concepts of the equation of planes.
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