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 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 Exercise 10.1 :Vector Algebra

NCERT Solutions Exercise 10.2: Vector Algebra

NCERT Solutions Exercise 10.3 Vector Algebra

NCERT Solutions Exercise Miscellaneous: Vector Algebra

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

Q1. Findย  ย  ย ,ifย  and .

Solutions: We are given that

,ย

Q2.Find a unit vector perpendicular to each of the vectorย  ย  and, whereย  ย  andย

Solutions: We are givenย  vectorsย  ย  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 vectorย  makes an angle ฯ/3 withย  , ฯ/4,ย  withย  and an acute angle ฮธ with , then find ฮธ and hence ,the components of

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

Therefore

Since is a unit vector

It is also given that ย ย  makes an angle ฯ/3 withย  , ฯ/4,ย  withย  and an acute angle ฮธ with

We know that

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

Similarly, we can get

Now, we have

Squaring both sides

cosยฒฮธ + 3/4 =1

cosยฒฮธ =1/4

cos ฮธ = 1/2โa3=1/2

Hence components of are 1/2,1/โ2 and 1/2

Q4. Show thatย

Solution: Taking LHS

By the distributive property of the vector product

Q5.Find ฮป andย ฮผ if

Solutions:We are given that

Simplifying it

Comparing both sides

6ฮผ – 27ฮป = 0….(i) ,2ฮผย  – 27=0…..(ii), 2ฮป – 6 = 0…….(iii)

From equation (ii) , (ii)

ฮผ = 27/2, ฮป = 3 and

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

Solution: It is given that

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

It is also given that

Equation (ii) implies that either ย  or sin ฮธ=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 parallelย  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 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 scienceย

 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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 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 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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