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# NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra

NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra will help you to boost your maths preparation for the term 2 CBSE Board exam 2021-22. All the unsolved questions of the exercise 10.2 of chapter 10-Vector Algebra are solved by an expert of maths as per the CBSE norms, NCERT Solutions For Class 12 Maths Exercise 10.2: 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 the cost and download free PDFs.

What is differentiation?

### 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

Class 12 Solutions of Maths Latest Sample Paper Published by CBSE for 2021-22 Term 2

Class 12 Maths Important Questions-Application of Integrals

Class 12 Maths Important questions on Chapter 7 Integral with Solutions for term 2 CBSE Board 2021-22

Solutions of Class 12 Maths Question Paper of Preboard -2 Exam Term-2 CBSE Board 2021-22

Solutions of class 12  maths question paper 2021 preboard exam CBSE Solution

## NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra

Q1. Compute the magnitude of the following vectors:

Ans. Given vectors are

Q2. Write two different vectors having same magnitude.

Solution: Two vectors with the same magnitude are supposed be different when their directions are different.

Let one of the vector is

Then another vector that is equal to this vector but has a different direction is given by

Both of vector are different but equal in magnitude

Q3. Write two different vectors having same direction.

Solution: Let one of the vector is given by

Then another vector that has the same direction is given by

Direction cosines of vector  are l,m, and n are given by

Direction cosines of vector  are l,m, and n are given by

Both of the vectors have the same direction because both have the same direction cosines.

Q4. Find the values of x and y so that the vectors   and    are equal.

Solution: It is given that

If both vectors and are equal, then their components should be equal

Therefore x = 2 and y =3

Q5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).

Solution:

Let the given initial point is named P(2,1) and Q(-5,7)

Then the vector  is given by

Hence scaler component of the vector , are -7 and 6 while vector components are  and  .

Q6. Find the sum of  the vectors

Solutions: The given vectors are

Q7.Find the unit vector in the direction of the vector.

Solution:The unit vector ( )in the direction of the vector    is given by

Q8. Find the unit vector in the direction of the vector, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.

Solution: The given points are P(1, 2, 3) and Q(4, 5, 6)

The vector passing through the given points is given as

The unit vector in the direction of     is given as

Q9.For given vectors, and,   find the unit vector in the direction of the vector

Solution:

The given vectors are   and

The vector   is the sum of the given vectors

The unit vector in the direction of  the vector    is given as

Q10. Find a vector in the direction of vector  which has magnitude 8 units.

Solution: The unit vector in the direction of  the given vector  is given as

Since the  vector we have to determine is of the magnitude of 8

Therefore the vector in the direction of vector    is

Q11. Show that the vectors   and    are collinear.

Solutions: Two vectors are collinear when

Where λ is a scaler

Let the given vectors are

Where λ = -2

Therefore both vectors are collinear

Q12. Find the direction cosines of the vector  .

Solution: The direction cosines (l,m,n)of the given vector are given by

Q13. Find the direction cosines of the vector joining the points A (1, 2, –3) and B (–1, –2, 1) directed from A to B.

Solutions:

The given points are A (1, 2, –3) and B (–1, –2, 1)

Direction cosines (l,m,n) of the vector   are

Q14. Show that the vector   is equally inclined to the axes OX, OY, and OZ.

Solution: The given vector is

The direction cosines(l,m,n) are

Let the angles made by the given vector with OX, OY, and OZ are  α, β and γ,since we have got l=cosα, m = cosβ, n = cosγ

It is clear that the given vector is equally inclined to the axes OX, OY, and OZ.

## NCERT Solutions and CBSE notes for classes 9,10,11 and 12 of Maths and Science

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

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### NCERT Solutions for class 11 maths

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