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.
Evaluate: $ \tan^{-1} \left[ 2 \sin \left( 2 \cos^{-1} \frac{\sqrt{3}}{2} \right) \right]$

View Solution

2.
If $M$ and $N$ are square matrices of order 3 such that $\det(M) = m$ and $MN = mI$, then $\det(N)$ is equal to :

$-1$
1
$-m^2$
$m^2$

View Solution

3.
Let both $AB'$ and $B'A$ be defined for matrices $A$ and $B$. If the order of $A$ is $n \times m$, then the order of $B$ is:

$n \times n$
$n \times m$
$m \times m$
$m \times n$

View Solution

4.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

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5.
The integrating factor of the differential equation $ (x + 2y^3) \frac{dy}{dx} = 2y $ is:

$ e^{y^2} $
$ \frac{1}{\sqrt{y}} $
$ e^{-\frac{1}{y^2}} $
$ e^{y^2} $

View Solution

6.
Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{5 \sin x + 3 \cos x}{\sin x + \cos x} \, dx \]

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.
Evaluate: $ \tan^{-1} \left[ 2 \sin \left( 2 \cos^{-1} \frac{\sqrt{3}}{2} \right) \right]$

2.
If $M$ and $N$ are square matrices of order 3 such that $\det(M) = m$ and $MN = mI$, then $\det(N)$ is equal to :

3.
Let both $AB'$ and $B'A$ be defined for matrices $A$ and $B$. If the order of $A$ is $n \times m$, then the order of $B$ is:

4.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

5.
The integrating factor of the differential equation \( (x + 2y^3) \frac{dy}{dx} = 2y \) is:

6.
Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{5 \sin x + 3 \cos x}{\sin x + \cos x} \, dx \]

Similar Mathematics Concepts

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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.Evaluate: $ \tan^{-1} \left[ 2 \sin \left( 2 \cos^{-1} \frac{\sqrt{3}}{2} \right) \right]$

2.If $M$ and $N$ are square matrices of order 3 such that $\det(M) = m$ and $MN = mI$, then $\det(N)$ is equal to :

3.Let both $AB'$ and $B'A$ be defined for matrices $A$ and $B$. If the order of $A$ is $n \times m$, then the order of $B$ is:

4. Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

5.The integrating factor of the differential equation \( (x + 2y^3) \frac{dy}{dx} = 2y \) is:

6. Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{5 \sin x + 3 \cos x}{\sin x + \cos x} \, dx \]

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Evaluate: $ \tan^{-1} \left[ 2 \sin \left( 2 \cos^{-1} \frac{\sqrt{3}}{2} \right) \right]$

2.
If $M$ and $N$ are square matrices of order 3 such that $\det(M) = m$ and $MN = mI$, then $\det(N)$ is equal to :

3.
Let both $AB'$ and $B'A$ be defined for matrices $A$ and $B$. If the order of $A$ is $n \times m$, then the order of $B$ is:

4.
Evaluate : \[ I = \int_0^{\frac{\pi}{4}} \frac{dx}{\cos^3 x \sqrt{2 \sin 2x}} \]

5.
The integrating factor of the differential equation \( (x + 2y^3) \frac{dy}{dx} = 2y \) is:

6.
Evaluate: \[ \int_0^{\frac{\pi}{2}} \frac{5 \sin x + 3 \cos x}{\sin x + \cos x} \, dx \]