NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.3

NCERT Solutions for Class 12 Maths Chapter 11 Three-dimensional Geometry Exercise 11.3 is covered in this article. This exercise of Chapter 11 deals with Plane, Coplanarity of Two Lines, Angle between Two Planes, Distance of a Point from a Plane, Angle between a Line and a Plane. NCERT Solutions for Class 12 Maths Chapter 11 will carry a weightage of around 7-14 marks in the CBSE Term 2 Exam 2022. NCERT has provided a total of 14 problems and solutions based on the important topics of the exercise.

Download PDF NCERT Solutions for Class 12 Maths Chapter 11 Integrals Exercise 11.3

NCERT Solutions for Class 12 Maths Chapter 11: Important Topics

Important topics covered in the Three-dimensional Geometry Chapter are:

Angle between two lines

Plane

Angle between line and plane

Angle between two vectors

Coplanarity

Also check: NCERT Solutions for Class 12 Maths Chapter 11 Three-dimensional Geometry

Other Exercises Solutions of Class 12 Maths Chapter 11 Three-dimensional Geometry

Exercise 11.1 Solutions	5 Questions
Exercise 11.2 Solutions	17 Questions
Exercise 11.3 Solutions	14 Questions
Miscellaneous Exercise Solutions	23 Questions

Chapter 11 Three-dimensional Geometry:

Angle between a Line and a Plane	Equation Line	Angle Between Two Vectors
Angle between Two Planes	Geometry	Plane
Coplanarity two lines	Section formula 3 dimension	Section formula 3 dimension

CBSE Class 12 Mathematics Study Guides:

NCERT Solutions for Class 12 Maths	Maths MCQs	Maths Syllabus
Mathematics Notes	Trigonometry	Maths Study Material
Arithmetic	Calculus	Algebra

CBSE CLASS XII Related Questions

1.
The area of the shaded region (figure) represented by the curves $ y = x^2 $, $ 0 \leq x \leq 2 $, and the y-axis is given by:

$ \int_0^2 x^2 \, dx $
$ \int_0^2 \sqrt{y} \, dy $
$ \int_0^4 x^2 \, dx $
$ \int_0^4 \sqrt{y} \, dy $

View Solution

2.
If vector $ \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} $ \text{ and } $ \mathbf{b} = \hat{i} - \hat{j} + \hat{k} $, then which of the following is correct?

$ \mathbf{a} \parallel \mathbf{b} $
$ \mathbf{a} \perp \mathbf{b} $
$ |\mathbf{a}|>|\mathbf{b}| $
$ |\mathbf{a}| = |\mathbf{b}| $

View Solution

3.
Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.

View Solution

4.
For a function $f(x)$, which of the following holds true?

$\int_a^b f(x) dx = \int_a^b f(a + b - x) dx$
$\int_a^b f(x) dx = 0$, if $f$ is an even function
$\int_a^b f(x) dx = 2 \int_0^a f(x) dx$, if $f$ is an odd function
$\int_0^a f(x) dx = \int_0^a f(2a + x) dx$

View Solution

5.
If \[ A = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}, \] then $ A^3 $ is:

$ \begin{bmatrix} 125 & 0 \\ 0 & 125 \end{bmatrix} $
$ \begin{bmatrix} 0 & 125 \\ 0 & 125 \end{bmatrix} $
$ \begin{bmatrix} 15 & 0 \\ 0 & 15 \end{bmatrix} $
$ \begin{bmatrix} 5^3 & 0 \\ 0 & 5^3 \end{bmatrix} $

View Solution

6.
The given graph illustrates:

$y = \tan^{-1} x$
$y = \csc^{-1} x$
$y = \cot^{-1} x$
$y = \sec^{-1} x$

View Solution

NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.3

NCERT Solutions for Class 12 Maths Chapter 11: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 11 Three-dimensional Geometry

CBSE CLASS XII Related Questions

1.
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:

2.
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?

3.
Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.

4.
For a function $f(x)$, which of the following holds true?

5.
If \[ A = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}, \] then \( A^3 \) is:

6.
The given graph illustrates:

Similar Mathematics Concepts

Comments

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NCERT Solutions for Class 12 Maths Chapter 11 Three Dimensional Geometry Exercise 11.3

NCERT Solutions for Class 12 Maths Chapter 11: Important Topics

Other Exercises Solutions of Class 12 Maths Chapter 11 Three-dimensional Geometry

CBSE CLASS XII Related Questions

1.The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:

2.If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?

3.Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.

4.For a function $f(x)$, which of the following holds true?

5.If \[ A = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}, \] then \( A^3 \) is:

6.The given graph illustrates:

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The area of the shaded region (figure) represented by the curves \( y = x^2 \), \( 0 \leq x \leq 2 \), and the y-axis is given by:

2.
If vector \( \mathbf{a} = 3 \hat{i} + 2 \hat{j} - \hat{k} \) \text{ and } \( \mathbf{b} = \hat{i} - \hat{j} + \hat{k} \), then which of the following is correct?

3.
Let \[ A = \begin{pmatrix} 1 & 4 \\ -2 & 1 \end{pmatrix} \quad \text{and} \quad C = \begin{pmatrix} 3 & 4 & 2 \\ 12 & 16 & 8 \\ -6 & -8 & -4 \end{pmatrix}. \] Then, find the matrix $B$ if $AB = C$.

4.
For a function $f(x)$, which of the following holds true?

5.
If \[ A = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}, \] then \( A^3 \) is:

6.
The given graph illustrates: