RS Aggarwal Class 12 Chapter 27 Solutions (Straight Line In Space)
RS Aggarwal Solutions for Class 12 Chapter 27 Straight Line in Space has sizeable weightage in Class 12 CBSE Board Exam and other competitive entrance exams like JEE and NEET. In this Chapter of RS Aggarwal Solutions, we will revisit the concepts of a straight line, and we will also learn about the ways in which a straight line can be uniquely determined and the cartesian representation of its vector form. You will be amazed to learn about non-intersecting and non-parallel lines which are termed as skew lines and the shortest distance between the lines and their cartesian form of representation besides developing an understanding about the angles between two straight lines.
There are 119 questions in 7 exercises in the RS Aggarwal Class 12 Solutions of Chapter 27 Straight line in Space. These questions range from beginner level to high-level and therefore, the exercise solutions are curated in such a manner that it will be adaptable for you to match the pace with the increasing level of complexity of problems. The exercise solutions are important for the objective entrance exams and the written subjective board exams both.
The answers for RS Aggarwal Class 12 Maths book are written by an expert team of math teachers at Instasolv. The mathematicians at Instasolv are well trained in the questions asked most frequently, therefore you will find these solutions very detailed and lucid at the same time. These solutions will meet all the demands related to the topics in this chapter. It is highly recommended that you read and practice the answers besides studying your course textbook for exams. You will be able to manage your time well after solving these questions which will boost your confidence and hence your marks significantly.
Important Topics Covered in RS Aggarwal Solutions for Chapter 27 – Straight Line in Space
Introduction to Straight Line in Space:
We have already understood the equation of a straight line in two dimensions. Now, we will study about the vector and cartesian representation of a straight line.
A straight line can be distinctly identified by either of the following two criteria:
- It has defined direction and passes through a given point.
- It passes through two designated points.
Equation of a straight line which passes through a defined point and in a given direction parallel to a vector b
If r is a position vector of a random point P on the given line and is a parameter while a be the vector of a point A with respect to the origin through which the given line passes; then,
Note: When b =ai+bj+ck then the direction ratios of the line are given by a, b, and c. Also, vice versa holds true, that is, if a, b , and c are direction ratios then b =ai+bj+ck will be parallel to a given line.
Cartesian form from the Vector Form:
When the direction cosines of a line are given by l, m and n, then the equation of the line can be given as
Equation of a line that passes through two given points:
If a and b are the position vectors of 2 given points A and B with coordinates (x1, y1, z1) and (x1, x2, x3) respectively and when r is a position vector of a random point P on the given line such that AP=r –a and AB=b –a are collinear vectors then the vector equation of the line is given as,
, where is a parameter and is a real number.
Cartesian Form from the Vector Form:
The Cartesian representation of the vector form can be given by the following equation for the points described in the above heading:
Key Points of the Chapter:
Angles between two Lines:
If θ is the angle between two lines L1 and L2 with their direction ratios as a1, b1, c1and a2, b2, c2respectively. Also, P and Q are points on the lines L1 and L2 such that the given angle is an acute angle between OP (if O is the origin) and OQ then, the angle is given as:
Distance between 2 points:
Exercises Discussion of RS Aggarwal Solutions for Class 12 Chapter 27 – Straight Line in Space
- There are 7 exercises in the RS Aggarwal Class 12 Chapter ‘Straight Line in Space’. Exercise 1 has 26 questions based on questions related to the vector and cartesian equations of straight lines.
- In exercise 2, you need to show that the given points are collinear.
- In exercise 3, there are 13 questions based on finding angles between pairs of straight lines.
- Exercise 4 has 19 questions where you need to find the shortest distance between two lines.
- In exercise 5, you are given 6 questions where you need to find the equation of the line and the shortest distance between the given set of points.
- In exercise 6, there are 23 very short answer questions on various concepts introduced in the chapter.
- The last exercise consists of objective-type questions to assist you in the revision of all the concepts learned in this chapter.
Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 27 by Instasolv
The language used by the experts at Instasolv is very easy to understand. RS Aggarwal Solutions for Class 12 Maths Chapter 27 will help you make efficient utilisation of your time by making you grasp more in lesser time. The answers at Instasolv are easily accessible on a user-friendly dashboard. Refer to them anytime you get stuck in any of the concepts of the chapter.