NCERT Solutions for Class 12 Maths Exercise 10.3 of Chapter 10 Vector Algebra

NCERT Solutions For Class 12 Maths Exercise 10.3: Vector Algebra will help you in the preparation of the term 2 CBSE Board exam 2021-22. All the unsolved questions of exercise 10.3 of chapter 10-Vector Algebra are solved by an expert of maths as per the CBSE norms, NCERT Solutions For Class 12 Maths Exercise 10.3: Vector Algebra is the most important input study material for the preparation of CBSE Board exam, engineering entrance exams, NDA, CBSE, and other UPSE entrance exams. You can study here all the study material free of cost and download free PDFs.

NCERT Solutions for Class 12 Maths Exercise 10.3 of Chapter 10 Vector Algebra

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NCERT Solutions Exercise 10.1 :Vector Algebra

NCERT Solutions Exercise 10.2: Vector Algebra

NCERT solutions for class 12 maths

Chapter 1-Relations and Functions	Chapter 9-Differential Equations
Chapter 2-Inverse Trigonometric Functions	Chapter 10-Vector Algebra
Chapter 3-Matrices	Chapter 11 – Three Dimensional Geometry
Chapter 4-Determinants	Chapter 12-Linear Programming
Chapter 5- Continuity and Differentiability	Chapter 13-Probability
Chapter 6- Application of Derivation	CBSE Class 12- Question paper of maths 2021 with solutions
Chapter 7- Integrals
Chapter 8-Application of Integrals

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Q1. Find the angle between two vectors and with magnitudes √3 and 2, respectively having

Solutions: Let the angle between both of the given vector  and is θ

We have

We are given

√6 = √3× 2 cos θ

cos θ = √6/2√3 = √2/2 = 1/√2

cos θ = cos π/4

θ = π/4

Therefore the angle between two vectors and is π/4

Q2. Find the angle between the vectors        and   

Solutions: Let the  both of the given vectors are

The magnitudes of the both vectors are

Let the angle between both of the vectors is θ

We have

10 = √14×√14 cos θ

cos θ = 10/14 = 5/7

θ = Cos^-1(5/7)

Therefore the angle between the given vectors is Cos^-1(5/7)

Q3. Find the projection of the vector on the vector  .

Solutions: Let the  both of the given vectors are

We have

Projection of  on is 

Q4.Find the projection of the vector   on the vector .

Solutions: Let the  both of the given vectors are

We have

Projection of  on is 

Q5.Show that each of the given three vectors is a unit vector:

Also, show that they are mutually perpendicular to each other.

Solutions: Let the   given vectors are

Therefore each of the given three vectors is a unit vector

Now, have

Similarly

Therefore the given three vectors are mutually perpendicular to each other.

Solution: It is given that

Simplifying it

Also given that

 

Q7. Evaluate the product   

Solution: Let’s find the product of the given vector

Q8.Find the magnitude of two vectors, having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2.

Solution: Let the angle between the given vector is θ

We are given that θ = 60°

Since

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NCERT Solutions of Science and Maths for Class 9,10,11 and 12

NCERT Solutions for class 9 maths

Chapter 1- Number System	Chapter 9-Areas of parallelogram and triangles
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3- Coordinate Geometry	Chapter 11-Construction
Chapter 4- Linear equations in two variables	Chapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s Geometry	Chapter 13-Surface Areas and Volumes
Chapter 6-Lines and Angles	Chapter 14-Statistics
Chapter 7-Triangles	Chapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundings	Chapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?	Chapter 10- Gravitation
Chapter3- Atoms and Molecules	Chapter 11- Work and Energy
Chapter 4-Structure of the Atom	Chapter 12- Sound
Chapter 5-Fundamental unit of life	Chapter 13-Why do we fall ill ?
Chapter 6- Tissues	Chapter 14- Natural Resources
Chapter 7- Diversity in living organism	Chapter 15-Improvement in food resources
Chapter 8- Motion	Last years question papers & sample papers

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NCERT Solutions for class 10 maths

Chapter 1-Real number	Chapter 9-Some application of Trigonometry
Chapter 2-Polynomial	Chapter 10-Circles
Chapter 3-Linear equations	Chapter 11- Construction
Chapter 4- Quadratic equations	Chapter 12-Area related to circle
Chapter 5-Arithmetic Progression	Chapter 13-Surface areas and Volume
Chapter 6-Triangle	Chapter 14-Statistics
Chapter 7- Co-ordinate geometry	Chapter 15-Probability
Chapter 8-Trigonometry

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NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equations	Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt	Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals	Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds	Chapter 12- Electricity
Chapter 5-Periodic classification of elements	Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process	Chapter 14-Sources of Energy
Chapter 7-Control and Coordination	Chapter 15-Environment
Chapter 8- How do organisms reproduce?	Chapter 16-Management of Natural Resources

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NCERT Solutions for class 11 maths

Chapter 1-Sets	Chapter 9-Sequences and Series
Chapter 2- Relations and functions	Chapter 10- Straight Lines
Chapter 3- Trigonometry	Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction	Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities	Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations	Chapter 15- Statistics
Chapter 8- Binomial Theorem	Chapter 16- Probability

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