## Revision Notes for CBSE Class 11 Maths Chapter 11 (Introduction to Three Dimensional Geometry) - Free PDF Download

## FAQs on Introduction to Three Dimensional Geometry Class 11 Notes CBSE Maths Chapter 11 [Free PDF Download]

1. Find the direction cosines of a line that makes angles measuring 90 degrees, 135 degrees, and 45 degrees with the x, y, and z axes, respectively.

Let’s assume that the direction cosines of the line are l, m, and n.

In this question, the value of α = 90 degrees, β = 135 degrees, and γ = 45 degrees

We also know that l = cos α, m = cos β, and n = cos γ

This means that the directions of cosine are:

L = cos 90 = 0

M = cos 135 = cos (180 - 45) = -cos 45 = -1 / √2

N = cos 45 = 1 / √2

Hence, the directions cosines of the line are 0, -1 / √2, and 1 / √2

2. Prove that the points (2, 3, 4), (-1, -2, 1), and (5, 8, 7) are collinear

The lines can also be collinear if the direction ratios of the two line segments are proportional to one another.

This means that if assume that the given points are: A (2, 3, 4), B (-1, -2, 1), and C (5, 8, 7), then the direction ratio of the line that is joining the points A (2, 3, 4) and B (-1, -2, 1) can be represented by: ((-1 -2), (-2 -3), (1 - 4)) = (-3, -5, -3)

Here, a_{1} = -3, b_{1} = -5, and c_{1} = -3

The direction ratio of the line that is joining the points B (-1, -2, 1) and C (5 8, 7) is:

[(5 - (-1), (8 - (-2)), (7 - 1)] = (6, 10, 6)

Here, a_{2} = 6, b_{2} = 10, and c_{2} = 6

From these equations it should be clear that the direction ratios of AB and BC are of the same proportions. Hence,

A_{2} / a_{1} = 6 / -3 = -2

B_{2} / b_{1} = 10 / -5 = -2

C_{2} / c_{1} = 6 / -3 = -2

This proves that the points A, B, and C are collinear.

3. From where can I download revision notes of Chapter 11 of Class 11 Maths?

Students can download the revision notes of Chapter 11 of Class 11 Maths from Vedantu. They can follow the given steps for the same:

Click on the given link CBSE Class 11 Chapter 11

As the link will open, you will find that the website of Vedantu will appear on your device screen.

On the page of Vedantu, you will find the notes of Chapter 11 of Class Maths.

The same page will provide you with the option of “Download PDF”.

Click that option and the PDF file will be downloaded.

4. What should I do to prepare for Chapter 11 of Class 11 Maths?

If the students will follow the provided tips then they can easily prepare Chapter 11 of Class 11 Maths:

You should study this chapter from the NCERT book as the content is written in very simple language.

Solve each example and exercise to comprehend the concepts easily.

Clarify your doubts as soon as possible. If you'll not clear your doubts then there will be chances that you do not understand the chapter.

Refer to guidebooks or reference books to solve various types of questions and to know about the exam pattern.

5. What do you understand by the term rectangular coordinate system?

The term rectangular coordinate system is defined as the three lines which are perpendicular to each other. These lines have a common intersecting point. The names of the lines are as follows:

X-axis

Y-axis

Z-axis

The central point is written as “O”.

Using this system one can find the distance of the object kept in the 3D plane or space.

For example, position coordinates (4, 5, 6) means that the object has moved 4 units along the positive x-axis, 5 units along the positive y-axis and 6 units along the positive z-axis.

If you want to understand these concepts more accurately then go through the given link CBSE Class 11 Chapter 11. This link will redirect you to the official website of Vedantu where you can access the content related to Chapter 11 for free. Additionally, you can also download its PDF if you want to study offline.

6. Explain the coordinates of the point in space.

The rectangular coordinate system helps in locating the position of a point. These coordinates are measured at perpendicular distances from the three planes. These planes are:

XY Plane

YZ Plane

ZX Plane

The coordinates measured for the point are:

(x, 0, 0) is measured from the x-axis.

(0, y, 0) is measured from the y-axis.

(0, 0, z) is measured from the z-axis

Coordinates measured from the XY plane are (x, y, 0)

Coordinates measured from the YZ plane are (0, y, z)

Coordinates measured from the ZX plane are (x, 0, z)

7. What study materials should be considered by students to prepare Chapter 11 of Class 11 Maths?

For the preparation of exams, students do not understand how and from where they have to study. For a few students, Chapter 11 of Class 11 Maths is very difficult to prepare. Thus they are advised to study from the Maths NCERT book. This book contains lots of questions which will help you to understand the chapter if you solve them. Also, the language of this book is easy to comprehend. Students can also use other reference books for a better understanding of the concepts.