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RS Aggarwal Class 12 Chapter 26 Solutions (Fundamental Concepts of 3-Dimensional Geometry)

RS Aggarwal Solutions for Class 12 Chapter 26 ‘Fundamental Concepts of 3-D Geometry’ are prepared to help you in solving the exercise questions. The topics that are covered in this chapter include the distance between two points, division of a line joining two points, direction cosines and direction ratios of a straight line in the cartesian plane and the area of a triangle. This chapter is crucial in building a strong foundation for the understanding of the chapters ahead such as plane and straight line in space.

There are 18 questions compiled in one exercise. The questions will help you to establish the relationship between direction ratios and direction cosines with the properties that a straight line might exhibit such as collinearity, parallel to one another, etc. These questions will help you practice thoroughly before your school exams and will aid you in understanding the pattern of the questions asked both in the board exams or competitive exams such as NEET, BITSAT, and other entrance exams.

The expert maths faculty at Instasolv have created the answers to RS Aggarwal Solutions for Chapter 26 exercises based on research work about the most recurring doubts among students. You will find all the answers to even the most basic doubts that might arise while coming across certain problems. The team of Instasolv has worked hard to give you the answers that are compliant to the latest CBSE guidelines and trends in the exams of your level.

Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 26

Concepts of 3-D Geometry

The angle between a Line and a Plane:

Cartesian Form:

The cartesian form can be represented for a straight line and a plane respectively in mathematical form through the following equations,

For a straight line:

And for a plane:

You can also figure out the angle between the line and the given plane using the following equation:

Vector Form: While in vector form the angle between the plane that is represented such that r = a λ +b and the line that is given in the vector form as r *. n = d is given as:

Angle Between Two Lines:

The cosine of the angle made by any line on the three axes respectively are known as direction cosines and are given by l, m, n.

If you assume two lines with the direction cosines as (l2,m2,n2) and (l2,m2,n2)

If θ is the angle between these given lines then their cosine can be given by the following formula:

If it is essential for you to find the angle in terms of Sin, you may evaluate it using the trigonometric formula:

sin2θ = 1 – cos2θ

An important point to note here is that we have considered the lines to be passing through the origin.

Direction Cosine:

The direction cosine of a vector r can be given as,

Direction Ratios:

1 = (x2 + y2 + z2)/ r2 = l2 + m2 + n2

Hence, we conclude that the sum of the squares of all the direction cosines of a straight line is equal to 1.

Highlights:

  • Cartesian Form For a straight line:

And for a plane:

  • Direction cosine:

  • The sum of the squares of all the direction cosine of a straight line is equal to 1

Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 26 – Fundamental Concepts of 3-D Geometry

  1. The exercise solutions in this chapter will require you to be able to connect the concepts of direction ratios and direction cosines with collinearity, parallel lines, therefore it will help varnish your knowledge about the vectors and geometry attained until now.
  2. The exercises in this chapter have questions of all levels in an increasing difficulty order to help you adjust to the complex topics.
  3. Solving this chapter’s exercise questions will prepare you for the chapters carrying a high weightage in your exams. Therefore, it is very essential that you attain clarity in the concepts of this chapter.
  4. It is advised that you use RS Aggarwal Class 12 Chapter 26 solutions as a source of reference with your NCERT textbooks to get good marks in the exam.
  5. To get a rank in the competitive exams, it is important that you solve these questions rigorously.

Perks of RS Aggarwal Solutions for Class 12 Maths Chapter 26 by Instasolv

The subject matter experts of Instasolv have prepared the answers strictly in line with CBSE guidelines. At Instasolv, you will find the answers to all the queries that may possibly arise while solving the problems of RS Aggarwal Class 12 Maths Solutions. You can rely on our platform completely as all the questions have been covered without any compromise with the quality of reasoning in the answers.