**NCERT Solutions for Class 12 Maths Exercise 10.3 of Chapter 10 Vector Algebra**

NCERT Solutions For Class 12 Maths Exercise 10.3: Vector Algebra will help you in the preparation of the term 2 CBSE Board exam 2021-22. All the unsolved questions of exercise 10.3 of chapter 10-Vector Algebra are solved by an expert of maths as per the CBSE norms, NCERT Solutions For Class 12 Maths Exercise 10.3: 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 cost and download free PDFs.

**NCERT Solutions for Class 12 Maths Exercise 10.3 of Chapter 10 Vector Algebra**

**NCERT Solutions Exercise 10.1 :Vector Algebra**

**NCERT Solutions Exercise 10.2: Vector Algebra**

**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**

**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**

**Q1. Find the angle between two vectors ****and ****with magnitudes √3 and 2, respectively having**

Solutions: Let the angle between both of the given vector ** ****and **** is θ**

We have

We are given

√6 = √3× 2 cos θ

cos θ = √6/2√3 = √2/2 = 1/√2

cos θ = cos π/4

θ = π/4

Therefore the angle between two vectors and is π/4

**Q2. Find the angle between the vectors and **

Solutions: Let the both of the given vectors are

The magnitudes of the both vectors are

Let the angle between both of the vectors is θ

We have

10 = √14×√14 cos θ

cos θ = 10/14 = 5/7

θ = Cos^{-1}(5/7)

Therefore the angle between the given vectors is Cos^{-1}(5/7)

**Q3. Find the projection of the vector **** on the vector ****.**

Solutions: Let the both of the given vectors are

We have

Projection of ** ****on **** is **

**Q4.Find the projection of the vector ****on the vector ****.**

Solutions: Let the both of the given vectors are

We have

Projection of ** ****on **** is **

**Q5.Show that each of the given three vectors is a unit vector:**

**Also, show that they are mutually perpendicular to each other.**

Solutions: Let the given vectors are

Therefore each of the given three vectors is a unit vector

Now, have

Similarly

Therefore the given three vectors are mutually perpendicular to each other.

Solution: It is given that

Simplifying it

Also given that

**Q7. Evaluate the product **

Solution: Let’s find the product of the given vector

**Q8.Find the magnitude of two vectors****, having the same magnitude and such that the angle between them is 60° and their scalar product is 1/2.**

Solution: Let the angle between the given vector ** ** is θ

We are given that θ = 60°

Since

**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**

**Structure and Function of Cell : Cell Biology**

**Archimedes Principle: Complete detail**

**Average Speed and Average velocity**

**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**

**Determining Valency, Net Charge and Molecular Formula**

**Ozone Layer and How it is Getting depleted.**

**Human Eye – Structure and functions**

**Myopia, Hypermetropia, and Presbyopia**

**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**

**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**

**NCERT Solutions for class 9 science **

**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**

**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**

**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**