# 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 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 a_{1},a_{2} and a_{3}

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 = 1/2โa_{3}=1/2

Hence components of are 1/2,1/โ2 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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