NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra - Future Study Point

NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra

NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra

NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra

 

NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra

NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra is compulsory to study for clearing the concept of vector algebra of class 12 maths NCERT.NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra will help students for the preparation of the maths paper for the CBSE Board exam term 2. All the unsolved questions of exercise 10.4 of chapter 10 Vector Algebra are created by a CBSE Maths expert as per the CBSE norms.Here you can study all the study material, NCERT Solutions, Science and Maths notes, preparation for the competitive entrance exams, and e-books free of cost.

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NCERT Solutions for Class 12 Maths Exercise 10.4 of Chapter 10 Vector Algebra

 

Q1. Find     ,if  and .

Solutions: We are given that

Q2.Find a unit vector perpendicular to each of the vector    and, where    and 

Solutions: We are given  vectors    and, where

,

The unit vector that is perpendicular to both vectors = cross product of both vectors/Magnitude of the cross product of both vectors

The unit vector that is perpendicular to both vectors

Q3.If a unit vector  makes an angle π/3 with  , π/4,  with  and an acute angle θ with , then find θ and hence ,the components of

Solution: Let the unit vector  has the components a1,a2 and a3

Therefore

Since is a unit vector

It is also given that    makes an angle π/3 with  , π/4,  with  and an acute angle θ with

We know that

and ,two vectors that makes an angle θ with each other then we have

Similarly, we can get

Now, we have

Squaring both sides

cos²θ + 3/4 =1

cos²θ =1/4

cos θ = 1/2⇒a3=1/2

Hence components of are 1/2,1/√2 and 1/2

Q4. Show that 

Solution: Taking LHS

By the distributive property of the vector product

Q5.Find λ and μ if

Solutions:We are given that

Simplifying it

Comparing both sides

6μ – 27λ = 0….(i) ,2μ  – 27=0…..(ii), 2λ – 6 = 0…….(iii)

From equation (ii) , (ii)

μ = 27/2, λ = 3 and

Q6.Given that     and ,what can you conclude about the vectors and ?

Solution: It is given that

 

Equation (i) implies that either   or cos θ=0(i.e both vectors are perpendicular to each other)

It is also given that

Equation (ii) implies that either   or sin θ=0(i.e both vectors are parallel to each other)

From Equation (i) and Equation (ii), it is to be concluded that both vectors can’t be parallel  and perpendicular simultaneously.

Therefore

Q7. Let the vectors given as , , , then show that

Solutions:

The given vectors are , ,

Evaluating LHS

First of all evaluating

Now, simplifying LHS

 

 

……..(i)

Simplifying RHS

……(ii)

And

…….(iii)

Adding (ii) and (iii) equations

Hence

Q8. If either or then .Is the converse true?Justify your answer with an example.

Solution:

We are given that if either or then .

Let’s prove if then or

Taking two vector and parallel to each other

Let

Hence converse of the given situation is not true.

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NCERT Solutions for class 9 maths

Chapter 1- Number SystemChapter 9-Areas of parallelogram and triangles
Chapter 2-PolynomialChapter 10-Circles
Chapter 3- Coordinate GeometryChapter 11-Construction
Chapter 4- Linear equations in two variablesChapter 12-Heron’s Formula
Chapter 5- Introduction to Euclid’s GeometryChapter 13-Surface Areas and Volumes
Chapter 6-Lines and AnglesChapter 14-Statistics
Chapter 7-TrianglesChapter 15-Probability
Chapter 8- Quadrilateral

NCERT Solutions for class 9 science 

Chapter 1-Matter in our surroundingsChapter 9- Force and laws of motion
Chapter 2-Is matter around us pure?Chapter 10- Gravitation
Chapter3- Atoms and MoleculesChapter 11- Work and Energy
Chapter 4-Structure of the AtomChapter 12- Sound
Chapter 5-Fundamental unit of lifeChapter 13-Why do we fall ill ?
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Chapter 1-Real numberChapter 9-Some application of Trigonometry
Chapter 2-PolynomialChapter 10-Circles
Chapter 3-Linear equationsChapter 11- Construction
Chapter 4- Quadratic equationsChapter 12-Area related to circle
Chapter 5-Arithmetic ProgressionChapter 13-Surface areas and Volume
Chapter 6-TriangleChapter 14-Statistics
Chapter 7- Co-ordinate geometryChapter 15-Probability
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Chapter 1- Chemical reactions and equationsChapter 9- Heredity and Evolution
Chapter 2- Acid, Base and SaltChapter 10- Light reflection and refraction
Chapter 3- Metals and Non-MetalsChapter 11- Human eye and colorful world
Chapter 4- Carbon and its CompoundsChapter 12- Electricity
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Chapter 7-Control and CoordinationChapter 15-Environment
Chapter 8- How do organisms reproduce?Chapter 16-Management of Natural Resources

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Chapter 1-SetsChapter 9-Sequences and Series
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NCERT solutions for class 12 maths

Chapter 1-Relations and FunctionsChapter 9-Differential Equations
Chapter 2-Inverse Trigonometric FunctionsChapter 10-Vector Algebra
Chapter 3-MatricesChapter 11 – Three Dimensional Geometry
Chapter 4-DeterminantsChapter 12-Linear Programming
Chapter 5- Continuity and DifferentiabilityChapter 13-Probability
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