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.

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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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

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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
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Chapter 1- Chemical reactions and equations	Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt	Chapter 10- Light reflection and refraction
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Chapter 5-Periodic classification of elements	Chapter 13-Magnetic effect of electric current
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Chapter 7-Control and Coordination	Chapter 15-Environment
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Chapter 5-Complex numbers	Chapter 13- Limits and Derivatives
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