##### Tallentex 2025 - ALLEN's Talent Encouragement Exam

ApplyRegister for Tallentex '25 - One of The Biggest Talent Encouragement Exam

Edited By Lovekush kumar saini | Updated on Jan 25, 2022 09:47 AM IST

RD Sharma books are considered to be the best option for exam preparation. They are used by a majority of CBSE schools all over the country. RD Sharma books are well known to be comprehensive and informative which is why they are used extensively for setting up question papers.

**Also Read -** RD Sharma Solutions For Class 9 to 12 Maths

- The RD Sharma class 12th exercise 27.2 is used by thousands of students and teachers for the practical knowledge of maths. The RD Sharma class 12 solution of Straight line in space exercise 27.2 consists of 36 questions covering all the concepts which are
Prove the lines are mutually perpendicular

lines through the points are perpendicular to the line through the points

lines through the points are parallel to the line through the points

The angle between the pair of lines given in vector and cartesian form

Equation of line passing through the points

Perpendicularity of two lines

Straight Line in Space Exercise 27.2 Question 1

so all the three dimensions cosines are mutually perpendicular to each other .

Straight Line in Space Exercise 27.2 Question 2

Direction ratio of

For showing perpendicular,

Now

Hence line1 and line2 are perpendicular to the points (showed)

Straight Line in Space Exercise 27.2 Question 3

**Answer:** The given two lines will be parallel through the two points equal to ‘0’ showed;

**Given:** Show that the line through the points is parallel to the line through the points

**Hint: **for showing parallel v_{1 }and v_{2 }must be equal to ‘0’

**Solution: **

**Now, **

So the two lines are parallel to each other

Straight Line in Space Exercise 27.2 Question 4

Given: find the Cartesian equation of the line which passes through the points and parallel to the given line by:

Hint: let the Cartesian equation will be :-

Solution:

now,

so the above line is parallel to and passes through the given points.

Straight Line in Space Exercise 27.2 Question 5

Direction: ratio

Vector

Again,

So the given two lines are perpendicular to each other (showed)

Straight Line in Space Exercise 27.2 Question 6

Direction ratiobecause line passes through origin

Now from

So the line joining to the point is perpendicular to the line joining by the determined points

Straight Line in Space Exercise 27.2 Question 7

So the equation will be

Straight Line in Space Exercise 27.2 Question 8(i)

The 1

If be an angle between the lines , so will be the angle between b1&b2

So,

The angle between the lines will be

Straight Line in Space Exercise 27.2 Question 8(ii)

Let ‘’ be the angle between points of lines

So the answer will be

Straight Line in Space Exercise 27.2 Question 8(iii)

Straight Line in Space Exercise 27.2 Question 9(i)

Directon ratio

Direction vector

Again

Direction vector

So the answer will be

Straight Line in Space Exercise 27.2 Question 9(ii)

The angle between the points will be

Straight Line in Space Exercise 27.2 Question 9(iii)

**Solution:**

Again:

So the angle between the lines will be

Straight Line in Space Exercise 27.2 Question 9(iv)

So the angle will be

Straight Line in Space Exercise 27.2 Question 9(v)

again,

So the angle will be

Straight Line in Space Exercise 27.2 Question 10(i)

The angle between the pairs of lines will be

Straight Line in Space Exercise 27.2 Question 10(ii)

So the angle between the pairs of lines will be

Straight Line in Space Exercise 27.2 Question 10(iii)

The angle between the pairs of lines will be

Straight Line in Space Exercise 27.2 Question 10(iv)

The angle between the pairs of lines will be

Straight Line in Space Exercise 27.2 Question 11

While

So the angle between the pairs will be

Straight Line in Space Exercise 27.2 Question 12

So the equation of the line passing through the point is

Straight Line in Space Exercise 27.2 Question 13

Now:

So the equation will be

Straight Line in Space Exercise 27.2 Question 14

Answer: the equation of the line passing through the point will beGiven: find the equation of the line passing through the pointand parallel to the line

Hint: for parallel equation will be:

Solution: direction ratio

∴the equation will be;

Straight Line in Space Exercise 27.2 Question 15

So, the equation of the line will be

Straight Line in Space Exercise 27.2 Question 16

Straight Line in Space Exercise 27.2 Question 17

Direction ratio of

Direction ratio of

Now

The equation will be

Straight Line in Space Exercise 27.2 Question 18

&

The equation will be

Straight Line in Space Exercise 27.2 Question 19

Direction

Direction

Therefore the two lines are perpendicular

Straight Line in Space Exercise 27.4 Question 12

Now

So, the vector equation will be

Straight Line in Space Exercise 27.2 Question 21

Answer : the value of the will beGiven: if the lines are perpendicular find the value of

Hint: Because lines are perpendicular

So

Solution: are perpendicular that means they =’’

So,

so the value will be

Straight Line in Space Exercise 27.2 Question 22

CD and AB are parallel. So it cannot make any angle

Straight Line in Space Exercise 27.2 Question 23

Answer: the value will be 1Given: find the value of so that the following lines are perpendicular to each other;

Hint: because lines are perpendicular.

Solution:

Therefore

so the answer will be ‘’

Straight Line in Space Exercise 27.2 Question 24

Direction ratio

Direction cosines =

Now, vector along the line;

So the answer will be

and cosines will be

Straight Line in Space Exercise 27.2 Question 25

Answer: the value of k will be ‘’Given: find the value of k so that the lines are perpendicular to each other.

Hint: when two lines are perpendicular then dot product will be equal to ‘’

Solution: from equ (i)

From equation (ii)

Since two straight lines are perpendicular to each other then

So the answer will be ‘’

Straight Line in Space Exercise 27.2 Question 26

= and passes through the points . Also find the angle between the given lines

Now parallel vectors are

From the question,

Solving (iv) and (v) we get

Therefore

Now putting the above makes in equation;

hence the vector equation is .

Class 12 RD Sharma chapter 27 exercise 27.2 material is prepared by a group of subject experts who have years of experience in the field. This material is updated to the latest version of the book. Students can use it as a guide for the textbook and prepare accordingly. Additionally, it follows the CBSE syllabus, which means that students can use it for their homework.

As maths is a vast subject, teachers can't cover all topics through their lectures. However, RD Sharma class 12th exercise 27.2 material covers all topics and contains solutions students can refer to and stay ahead of their class.

The benefits of RD Sharma class 12th exercise 27.2 material are:

**1. Easily accessible**

This material is available on Career360's website and can be accessed through any device with an internet connection. This makes it easily accessible for students as they can now study from the comfort of their homes.

**2. Convenient for revision**

As RD Sharma's class 12th exercise 27.2 material contains questions and answers in the same place, students can refer to it quickly and efficiently. This helps a lot for last-minute revision as they won't have to look up answers in the textbook.

**3. Saves time in preparation**

Students can take advantage of this material to save a lot of time in their preparation. In addition, as this material covers the entire syllabus, there is no other textbook they will need to study.

**4. Easier to understand**

RD Sharma class 12 solutions chapter 27 exercise 27.2 material contains expert-related answers that have step-by-step solutions. Students who are weak in maths can also cope up and score good marks in exams.

**5. Free of cost**

The best part about RD Sharma's class 12th exercise 27.2 material is that it is free of cost and can be accessed by anyone through Career360's website. Career360 has prepared this material to help students gain more knowledge and score good marks in exams.

**RD Sharma Chapter-wise Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. In what ways is the RD Sharma class 12th solution accommodating for me?

It tends to be beneficial all around on the off chance that you practice routinely and thoroughly consistently and try to individual test with the RD Sharma solutions and assess the imprints as needs are.

2. Are the issues in the RD Sharma solutions like the NCERT solution?

Indeed, the materials gave in the RD Sharma solutions are ready as per the NCERT to coordinate with the prospectus for board exams.

3. How can RD Sharma class 12 chapter 27 be helpful for me?

It can be a guide for the students who like to self-test themselves on their recent lessons. You can use the answers in the book to evaluate your responses and correct them accordingly.

4. What number of questions are there in class 12 RD Sharma chapter 27.2?

There are 36 questions in RD Sharma Solutions Class 12 RD Sharma chapter 27.2 exercise 27.2.

5. Is the RD Sharma class 12 chapter 27 of the latest version?

Yes, these solutions are regularly updated to correspond with the syllabus of NCERT textbooks, which helps crack public examinations.

Get answers from students and experts

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer!

As per latest 2024 syllabus. Study 40% syllabus and score upto 100% marks in JEE

News and Notifications

Back to top