NCERT Solutions for Class 12 Maths | Chapter 11: Three dimensional Geometry | Free PDF Download

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Class 12

Latest NCERT Solutions for Class 12 Maths | Chapter 11: Three dimensional Geometry | Free PDF Download

NCERT Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry:

If you are a Class 12 Maths student looking for an in-depth understanding of Three Dimensional Geometry, you have come to the right place. In this blog, we will provide you with a complete guide to NCERT Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry.

Introduction to Three Dimensional Geometry:

Three Dimensional Geometry is a branch of mathematics that deals with the study of objects in three-dimensional space. The concepts of Three Dimensional Geometry are crucial in fields such as physics, engineering, and computer graphics. The chapter covers topics such as Direction Cosines and Direction Ratios, Distance between two points, Section Formula, and Equation of a Line in Space.

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NCERT Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry

NCERT Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry provides step-by-step solutions to all the exercises in the textbook. The solutions are designed in a way that helps students understand the concepts better and apply them to solve problems.

Here is an overview of the topics covered in the chapter:

Direction Cosines and Direction Ratios: This section introduces the concept of direction cosines and direction ratios of a line in space. Students will learn how to find the direction cosines and direction ratios of a line passing through two points.

Distance between two points: In this section, students will learn how to find the distance between two points in three-dimensional space using the distance formula.

Section Formula: The section formula is used to find the coordinates of the point that divides a line segment joining two given points in a given ratio. This section explains how to find the coordinates of the point using the section formula.

Equation of a Line in Space: This section explains how to find the equation of a line in space using various methods, such as the point-slope form and the symmetric form.

Important Terms Every Student Must Know about Three Dimensional Geometry:

Direction Cosines and Direction Ratios:

Direction cosines and direction ratios are fundamental concepts in Three Dimensional Geometry. Direction cosines refer to the cosines of the angles made by a line with the positive directions of the coordinate axes. On the other hand, direction ratios refer to the ratios of the lengths of the line segments intercepted by the line on the coordinate axes. In this section, students will learn how to find the direction cosines and direction ratios of a line in space.

Distance between two points:

The distance formula for two points in the coordinate plane can be easily extended to three dimensions. In this section, students will learn how to find the distance between two points in three-dimensional space using the distance formula. This formula involves finding the square root of the sum of the squares of the differences in the x, y, and z-coordinates of the two points.

Section Formula:

The section formula is used to find the coordinates of the point that divides a line segment joining two given points in a given ratio. In this section, students will learn how to find the coordinates of the point using the section formula. This formula can be applied to any line segment in three-dimensional space.

Equation of a Line in Space:

In this section, students will learn how to find the equation of a line in space using various methods, such as the point-slope form and the symmetric form. The point-slope form involves finding the slope of the line and the coordinates of a point on the line. The symmetric form involves finding the direction ratios of the line and the coordinates of a point on the line.

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Applications of Three Dimensional Geometry:

Three Dimensional Geometry has a wide range of applications in fields such as physics, engineering, and computer graphics. For example, in physics, Three Dimensional Geometry is used to study the motion of objects in space. In engineering, it is used to design and analyze three-dimensional structures such as buildings and bridges. In computer graphics, it is used to create three-dimensional models of objects and characters in video games and movies.

Conclusion

NCERT Solutions Class 12 Maths Chapter 11 Three Dimensional Geometry is an essential chapter that provides students with a foundation in Three Dimensional Geometry. The chapter covers a range of topics, including direction cosines and direction ratios, distance between two points, section formula, and equation of a line in space. With the help of Oswaal Books, students can access high-quality study materials that will help them excel in their exams