## NCERT Solutions for Maths Chapter 11 Exercise 11.2 Class 11 - FREE PDF Download

## FAQs on NCERT Solutions for Class 11 Maths Chapter 11 - Introduction to Three-Dimensional Geometry Exercise 11.2

1. What topics are covered in NCERT Solutions for Class 11 Maths Chapter 11, Exercise 11.2?

The exercise focuses on the distance formula, section formula, and finding the midpoint of a line segment in three-dimensional geometry.

2. How does the distance formula work in 3D geometry?

The distance formula in 3D geometry calculates the distance between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ using:

\[d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}\]

3. What is the section formula in Three-Dimensional Geometry?

The section formula helps to find the coordinates of a point dividing a line segment joining two points in a specific ratio. For points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ divided in the ratio $m:n$, the coordinates are:

\[\left(\frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n}, \frac{mz_2 + nz_1}{m + n}\right)\]

4. How can I verify if three points are collinear in 3D geometry?

To verify collinearity, calculate the distances between consecutive points. If the sum of the two smaller distances equals the total distance between the endpoints, the points are collinear.

5. What is the midpoint formula in three-dimensional geometry?

The midpoint of a line segment joining two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ is given by:

\[\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}, \frac{z_1 + z_2}{2}\right)\]

6. How does solving Exercise 11.2 help in understanding 3D geometry?

Exercise 11.2 builds a strong understanding of spatial relationships in three dimensions by focusing on fundamental concepts like distances and points, which are essential for more complex topics like planes and vectors.

7. What type of questions are asked in Exercise 11.2 of Chapter 11?

The questions involve calculating distances between points, verifying collinearity, finding midpoints, and using the section formula to divide line segments in a given ratio.

8. Why is the section formula important in 3D geometry?

The section formula helps determine how a line segment is divided internally or externally, which is crucial in solving problems involving the division of space in 3D geometry.

9. Are there any real-life applications of the distance formula in 3D geometry?

Yes, the distance formula is widely used in physics, engineering, and computer graphics to calculate distances between objects in three-dimensional space.

10. How can Vedantu’s NCERT solutions help in mastering Exercise 11.2?

Vedantu’s NCERT solutions provide step-by-step explanations, helping students to understand and solve complex problems easily, thereby improving their performance in exams.