Class 12 RS Aggarwal Chapter-26 Fundamental Concepts of 3-Dimensional Geometry Solutions - Free PDF Download
FAQs on RS Aggarwal Class 12 Solutions Chapter-26 Fundamental Concepts of 3-Dimensional Geometry
1. How do the Vedantu solutions for RS Aggarwal Class 12 Chapter 26 help in solving problems on 3-Dimensional Geometry?
The RS Aggarwal solutions for this chapter provide detailed, step-by-step methods for every problem. They focus on building a strong foundation by clearly explaining how to apply fundamental formulas like the distance formula, section formula for internal and external division, and finding the coordinates of a centroid, ensuring you understand the correct procedure for each type of question.
2. What is the correct method to solve problems involving the distance between two points in 3D space as per this chapter?
The correct method, as shown in the solutions, involves these steps:
- Identify the coordinates of the two points, (x₁, y₁, z₁) and (x₂, y₂, z₂).
- Substitute these values directly into the 3D distance formula: D = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²].
- Systematically calculate the result to find the distance between the points. The solutions demonstrate this for various problem types.
3. Are the problem-solving techniques in these solutions suitable for the CBSE Class 12 Board Exam 2025-26?
Yes, the methods used in the RS Aggarwal solutions are fully aligned with the CBSE 2025-26 syllabus and examination pattern. They emphasise showing clear, logical steps, which is crucial for scoring full marks on the board exams. Following these solutions helps you present your answers in the expected format.
4. How do the solutions for this chapter explain the difference between a point on an axis and a point in a plane?
The solutions clearly illustrate this fundamental concept. For any point lying on an axis (e.g., the Y-axis), its other two coordinates (x and z) will be zero. In contrast, for a point lying in a plane (e.g., the YZ-plane), only the coordinate perpendicular to it (x) will be zero. This distinction is critical for correctly solving problems in 3D geometry.
5. Why is understanding octants important, and how do the solutions help with this concept?
Understanding octants is crucial because it helps you visualise a point's location in 3D space based on the signs of its coordinates. The solutions for this chapter break down how the combination of positive and negative signs for the x, y, and z coordinates determines which of the eight octants a point belongs to, providing a solid conceptual base for more complex spatial analysis.
6. Beyond just the formula, what is the significance of the centroid of a triangle in 3D geometry as explained in these solutions?
Beyond the calculation, the solutions help you understand that the centroid is the geometric centre or the 'average' position of the triangle's vertices in 3D space. By showing that its coordinates are the arithmetic mean of the vertices' coordinates, the solutions reinforce the concept of the centroid as a point of balance and concurrence of the medians, which is a key physical and geometric property.
7. How are problems related to collinear points solved in the RS Aggarwal solutions for this chapter?
The solutions demonstrate a key method for proving collinearity. Three points A, B, and C are collinear if the sum of the distances between two pairs of points equals the distance of the third pair (e.g., AB + BC = AC). The solutions guide you to calculate all three distances using the distance formula and then check if this condition is met, providing a definitive way to solve such problems.
