...

Future Study Point

NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra

NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra

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.

NCERT Solutions For Class 12 Maths Exercise 10.2: Vector Algebra

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

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

Download:Direct and Indirect Narration rules Tenses wise and Sentences wise

You can also study

Active Voice to Passive Voice Rules

Learn Tenses in English and translate Hindi sentences into English language

Download PDF-Learn Tenses in English and translate Hindi sentences into the English language

Download: PDFActive Voice to Passive Voice rules,tenses wise and sentences wise

You can also study

Percentage questions for competitive entrance exams with Solutions

NCERT Questions on mensuration helpful for competive entrance exams

Tips to get success in competitive exams

The best books for cracking the competitive entrance exams of CPO,NDA, IAS, CDS and Bank PO

Government jobs after 10 or 12 th pass : Qualify Entrance exams of SSC MTS and SSC CHSL

Science  Notes

What is the difference between virtual and real images?

Image formation by Convex and Concave Lenses

Image formation by Convex and Concave Mirrors

Difference between Convex and Concave lenses

What are the factors affecting evaporation?

How does the water kept in an earthen pot become cold during summer ?

Functioning of Soda-Acid Fire Extinguisher

What is DDT?

Structure and Function of Cell : Cell Biology

Three laws of motion

Archimedes Principle: Complete detail

Average Speed and Average velocity

Three equation of Motions

Recoil velocity of the gun

Mole concept

The second  law of motion

The universal  law of gravitational force

Thrust and Pressure : Difference

Evoporation,Vapourization and Latent heat

Important salts class 10 CBSE sceience notes

Reflection, Refraction, Dispersion, and Scattering

Atom, Molecule, and Atomicity

Determining Valency, Net Charge and Molecular Formula

Ozone Layer and How it is Getting depleted.

Human Eye – Structure and functions

Myopia, Hypermetropia, and Presbyopia

Why do the star twinkle?

Electric Current and Heating effect of Electric Current

Complete detail of electrical resistance and conductance

Type of Chemical Reactions with Complete detail

Class 10 chemistry Viva Voce Questions and Answers for CBSE Board 2020-21

What are the physical and chemical properties of metals?

Important maths notes

Tricks – How to write linear equations

Tricks- How to solve question from algebraic equations

Three ways of solving quadratic equation

Mean, Mode and Median

Solutions- Specific questions of mensuration

Finding the roots of the polynomial by Complete square method

Technics – Achieving 100% marks in Maths

You can compensate us

Paytm number 9891436286

The money collected by us will be used for the education of poor students who leaves their study because of a lack of money.

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 science 

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

CBSE Class 9-Question paper of science 2020 with solutions

CBSE Class 9-Sample paper of science

CBSE Class 9-Unsolved question paper of science 2019

NCERT Solutions for class 10 maths

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

CBSE Class 10-Question paper of maths 2021 with solutions

CBSE Class 10-Half yearly question paper of maths 2020 with solutions

CBSE Class 10 -Question paper of maths 2020 with solutions

CBSE Class 10-Question paper of maths 2019 with solutions

NCERT Solutions for Class 10 Science

Chapter 1- Chemical reactions and equations Chapter 9- Heredity and Evolution
Chapter 2- Acid, Base and Salt Chapter 10- Light reflection and refraction
Chapter 3- Metals and Non-Metals Chapter 11- Human eye and colorful world
Chapter 4- Carbon and its Compounds Chapter 12- Electricity
Chapter 5-Periodic classification of elements Chapter 13-Magnetic effect of electric current
Chapter 6- Life Process Chapter 14-Sources of Energy
Chapter 7-Control and Coordination Chapter 15-Environment
Chapter 8- How do organisms reproduce? Chapter 16-Management of Natural Resources

Solutions of Class 10 Science Sample Paper and Question Papers for Term-1 and Term 2 2021-22 CBSE Board

Solution of Class 10 Science Question Paper Preboard 2021-22:Term 2 CBSE Board Exam

Solutions of Class 10 Science Sample Paper Term-1 2021-22 CBSE Board

Class 10 Science Sample Paper for Term 2 CBSE Board Exam 2021-22 with Solution

Solutions of Class 10 Science Question Paper Preboard Examination (First) 2021 -22 Class 10 Science

CBSE Class 10 – Question paper of science 2020 with solutions

CBSE class 10 -Sample paper of Science 2020

NCERT Solutions for class 11 maths

Chapter 1-Sets Chapter 9-Sequences and Series
Chapter 2- Relations and functions Chapter 10- Straight Lines
Chapter 3- Trigonometry Chapter 11-Conic Sections
Chapter 4-Principle of mathematical induction Chapter 12-Introduction to three Dimensional Geometry
Chapter 5-Complex numbers Chapter 13- Limits and Derivatives
Chapter 6- Linear Inequalities Chapter 14-Mathematical Reasoning
Chapter 7- Permutations and Combinations Chapter 15- Statistics
Chapter 8- Binomial Theorem  Chapter 16- Probability

CBSE Class 11-Question paper of maths 2015

CBSE Class 11 – Second unit test of maths 2021 with solutions

 

 

Scroll to Top
Seraphinite AcceleratorOptimized by Seraphinite Accelerator
Turns on site high speed to be attractive for people and search engines.