RD Sharma Solutions for Class 11 Maths Chapter 28 - Free PDF Download
FAQs on RD Sharma Class 11 Maths Solutions Chapter 28 - Introduction to 3D coordinate geometry
1. How do the RD Sharma Class 11 Chapter 28 solutions help in solving problems on 3D coordinate geometry?
The RD Sharma Class 11 Maths solutions for Chapter 28 provide detailed, step-by-step methods for tackling problems related to three-dimensional geometry. They guide you on how to correctly apply fundamental concepts such as the distance formula and section formula in various scenarios. By following these solutions, students can build a strong conceptual foundation and learn the precise methodology required for their exams.
2. Are the problem-solving methods in RD Sharma Class 11 Maths Chapter 28 solutions aligned with the CBSE 2025-26 syllabus?
Yes, the solutions are fully aligned with the latest CBSE syllabus for the 2025-26 session. The methods focus on the core topics prescribed by NCERT, including coordinate axes and planes in three dimensions, coordinates of a point, distance between two points, and the section formula. The step-by-step approach ensures students learn the correct format for answering questions in board exams.
3. What is the correct method to apply the section formula for internal division as explained in RD Sharma Class 11 solutions?
The solutions for RD Sharma Chapter 28 explain a clear, systematic approach for applying the section formula. To find the coordinates (x, y, z) of a point dividing the line segment joining P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) in the ratio m:n internally, you should follow these steps:
- Identify the coordinates of the two given points and the division ratio.
- Apply the formula for each coordinate separately: x = (mx₂ + nx₁)/(m+n).
- Similarly, calculate y = (my₂ + ny₁)/(m+n).
- Finally, find z = (mz₂ + nz₁)/(m+n).
4. What types of problems are covered in the solutions for exercises like 28.1 and 28.2 in RD Sharma's Chapter 28?
The initial exercises in RD Sharma Chapter 28 primarily focus on foundational concepts. The solutions guide you through problems based on:
- Identifying the octant in which a given point lies based on the signs of its coordinates.
- Calculating the distance of a point from the coordinate planes (xy, yz, zx) and coordinate axes (x, y, z).
- Applying the distance formula to find the length of the line segment between two points in space.
- Solving problems to prove properties of geometrical figures like isosceles triangles, right-angled triangles, and parallelograms using the distance formula.
5. How can I determine the octant of a point like (-3, 1, -5) using the logic from RD Sharma Chapter 28 solutions?
The solutions explain that the octant is determined by the signs of the x, y, and z coordinates. For a point (x, y, z), you analyse the signs:
- The x-coordinate is negative (-3).
- The y-coordinate is positive (1).
- The z-coordinate is negative (-5).
6. How do the solutions for RD Sharma Chapter 28 demonstrate proving if three points are collinear using the distance formula?
The solutions illustrate a clear method for checking collinearity. For any three points A, B, and C, you must first calculate the distance between each pair of points using the 3D distance formula, resulting in distances AB, BC, and AC. The points are considered collinear if the sum of the lengths of any two segments equals the length of the third segment (e.g., if AB + BC = AC). The solutions provide step-by-step calculations to verify this condition for specific problems.
7. What is a common mistake to avoid when finding the centroid of a triangle in 3D, as per the problems in RD Sharma?
A common mistake when solving for the centroid of a triangle with vertices (x₁, y₁, z₁), (x₂, y₂, z₂), and (x₃, y₃, z₃) is incorrectly averaging the coordinates. The correct approach, as demonstrated in RD Sharma solutions, is to find the average of each coordinate type separately. The coordinates of the centroid (G) are given by G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3, (z₁ + z₂ + z₃)/3). Students should avoid mixing up the coordinates or dividing by a number other than 3.
