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RD Sharma books have always set parameters for board exams for a long time. This book is very important from an exam point of view because teachers assign question papers from this book most of the time. Rd Sharma Class 12th Exercise FBQ solutions that you find here are not the work of a single person but a team of subject experts who always thrive for student’s success. Class 12th RD Sharma Chapter 26 Exercise 26 FBQ Solutions will help a student to revise a bit faster and save a lot of time. This particular exercise has 18 questions or fill in the blanks.

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The concepts that are discussed in Rd Sharma Class 12th Exercise FBQ are Direction Cosines which include an easy way to identify the direction of a line in three-dimensional space, Direction ratios, directional angles, Projection of line segment, unit vector are also discussed in this exercise. RD Sharma Solutions All the topics are wonderfully covered for a quick revision for the student.

Chapter 26- Directions Cosines and Directions Ratios - Ex-26.1

Chapter 26- Directions Cosines and Directions Ratios - Ex-MCQ

Chapter 26- Directions Cosines and Directions Ratios - Ex-VSA

Hint:

Use Distance Formula

Given:

Point

To Find:

Distance of point P from y -axis

Solution:

The distance of the point from y-axis will be the perpendicular distance from point to y-axis whose co-ordinates are

Distance formula is

where

Therefore distance from y axis is

Direction Cosines and Direction Ratios exercise Fill in the blanks question 2

Hint:

Use Distance Formula

Given:

Point

To Find:

Distance of point P from z -axis

Solution:

The distance of the point from z-axis will be the perpendicular distance from point to z-axis whose co-ordinates are

Distance formula is

where

Therefore distance of the point from z axis is .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 3

Hint:

Direction cosine is cosine of angle made with the axes

Given:

are the angles made with axes.

To Find:

Direction cosine of the line

Solution:

Therefore, the direction cosine of the line are

Direction Cosines and Direction Ratios exercise Fill in the blanks question 4

Given:

Line makes angles

To Find:

Solution:

Direction cosine of a line making angles with co-ordinate axes are

Now, using the formula:

Therefore, value of

Direction Cosines and Direction Ratios exercise Fill in the blanks question 5

Given:

Line makes angles α,β, γ with x,y,z axes

To Find:

Solution:

Direction cosine of a line making angles α,β,y are

......(i)

Now as ....... (ii)

∴ Using above eq(ii) in (i), we get

Therefore, the value of .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 6

Answer :

Using property of direction cosine

Given:

Line makes angles with y and z axes is

Hence

To Find:

Angle made with x-axes?

Solution:

Direction cosine of a line making angle α,β,γ are

Therefore, the angle made by line with x -axis is .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 7

of a vector are direction ratio of that vector.

Given:

Vector?

To Find:

Direction cosine of vector.

Solution:

If Direction cosine and ane direction ratios, then

Therefore .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 8

Use property of direction cosine

Given:

To Find:

= angle with z-axis

Solution:

Since line makes angle with x and y axes, there direction cosines are

Therefore, the angle made with z -axls is .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 9

Length of projection = Length × Direction cosine

Given:

Projections on coordinate axes are 3,4,5

To Find:

Length of line segment

Solution:

Let Line segment PQ makes angle α,β,γ with x,y and z axes, such that length of projection in coordinate axes are:

Now by properties of direction cosine

Therefore, the total length of line segment is .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 10

Answer:

Hint:Use direction ratio to find direction cosine.

Given:

To Find:

vector

Solution:

Direction cosine is related to Direction ratio as

Therefore, the vector

Direction Cosines and Direction Ratios exercise Fill in the blanks question 11

Answer: -Hint:

Use direction ratio of the line

Given:

Points and

To Find:

Direction cosine of line joining point

Solution:

Let point and are joined to form line

Direction Ratio of line Position vector of Position vector of

Direction ratio of line

Direction Cosine of line are:

Therefore the direction cosine of the line segment are .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 12

Answer:Hint:

Use property of direction cosine.

Given:

Direction cosine of line

To Find:

Value of c

Solution:

Therefore the value of c is .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 13

Answer: Point

Hint:Use direction ratio to find direction cosine

Given:

To Find:

Point P

Solution:

Direction cosine is related to direction ratio as :

Now, Position vector of Position vector of

where x,y,z are the coordinate of P

Now

Comparing both

Therefore, the coordinate of point P are

Direction Cosines and Direction Ratios exercise Fill in the blanks question 14

Answer:Hint:

Dot product of two direction cosine two vectors

Given:

To Find:

Angle between two vectors

Solution:

Angle between two vectors with direction ratios is

given by

Therefore, the angle between two vectors is .

Direction Cosines and Direction Ratios exercise Fill in the blanks question 15

Use the property of direction cosine

Given:

Direction cosine

To Find:

Value of

Solution:

By property of direction cosine, we get

Direction Cosines and Direction Ratios exercise Fill in the blanks question 16

Answer:Hint:

Use property

Given:

To Find:

(Angle between line and z axis)

Solution:

If a line makes α,β,γ, then

......(i)

It is given that

Taking cosine both side

.......(ii)

Using the above equation (ii) in (i) we get

Therefore, the value of is

Direction Cosines and Direction Ratios exercise Fill in the blanks question 17

Answer: 4Hint:

Use the property

Given:

To Find:

Number of equally inclined lines

Solution:

If α,β,γ are the angles made by line with axes, then

Possible direction cosine are

Different set of direction cosine are

Therefore, 4 lines are equally inclined to axes.

Direction Cosines and Direction Ratios exercise Fill in the blanks question 18

Answer →

Hint :

In zx plane y-coordinate is zero and y coordinate of points divide line segment.

Given :

Points are

To find:

Ratio in which line is divided

Solution :

Let zx-plane divide the line segment in ratio

Using section formula,

Therefore, the zx plane divide the line in ratio

Rd Sharma Class 12th Exercise FBQ solutions will help every student, and they will be able to clear the concepts and learn according to an exam point of view. The benefits of these solutions are:

**1. Good grades are guaranteed:**

Career360's solutions are created by a team of experts who work together to provide perfect answers in the simplest way possible. Students who practise this material on a regular basis have a good chance of passing their board exams.

**2. Excellent for revising:**

Because RD Sharma Class 12 Solutions Chapter 26 ex 26 FBQ contains all of the solutions needed to get good grades, it is easy for students to review if they have any questions. A student can quickly refer to the problem they are having difficulty with by using the solved examples.

**3. Managing Your Time**

Due to time constraints, teachers do not teach all of RD Sharma's problems. As a result, RD Sharma Class 12 Solutions Directions Cosines and Direction Ratios Ex FBQ material is readily available to demonstrate capability.

**4. Simple to grasp**

These expert-created solutions are simple and easy to understand. As a result, students who are unfamiliar with the chapter can refer to this material to gain a thorough understanding starting from the beginning.

**5. Questions from the NCERT**

The questions in exams are usually from the NCERT. Teachers assign question papers based on NCERT textbooks, so it is necessary to learn NCERT concepts and solve questions. Rd Sharma Class 12th Chapter 26 Exercise FBQ solutions assist students in understanding and learning concepts as well as answering questions about RD Sharma Class 12 Solutions Chapter 26 ex FBQ.

**6. It is free of charge**

For the benefit of students, Career360 provides the entire solution for free. You can use it to help you prepare for your exams. Thousands of students have already signed up to be a part of the team, and you should do the same.

- 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

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Download E-book1. What is the direction cosines of a line in a 3D plane?

A (directed) line's direction cosines are the cosines of the angles formed by the line with the positive directions of the coordinate axes.

2. What is the direction angle?

The angles formed by a line intersecting the positive directions of the X, Y, and Z axes are known as directional angles.

3. Can I score good marks after studying from Rd Sharma Class 12th Exercise FBQ solutions?

Our RD Sharma Solutions for Class 12 are created in accordance with the most recent CBSE syllabus. Solving RD Sharma exercise questions with the assistance of RD Sharma Solutions will assist students in achieving high marks in the Class 12 board examination. It also includes key concepts and formulas to help you understand the chapter better.

4. Where can I search for RD Sharma Maths Solutions?

The RD Sharma questions are intended to be answered by the students themselves. If you get stuck on a problem or are unsure whether your answers are correct, you can view or download the RD Sharma Solutions from the Career360 website.

5. Is RD Sharma's book appropriate for CBSE Class 12?

The NCERT textbook is the most important study material or reference book for Class 12. After you have finished solving the NCERT textbook, you will need a lot of practice. Solving the **Rd Sharma Class 12th Exercise FBQ **questions will give you a lot of practice, which is important for CBSE Class 12 students.

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