KEAM Important Chapters 2023: Practice Chapter-wise Questions

September 19, 202239 Insightful Publications

**NCERT Solutions for Class 12 Chapter 10 Maths Vector Algebra**: The Class 12 Maths chapter on vector algebra solutions will help students understand the basic concepts associated with the topic. This solution set covers all the questions mentioned in the exercise and elaborately explains vector algebra formulas. Students preparing for CBSE 12 Board and JEE or other engineering-based entrance examinations can refer to this solution set.

CBSE Class 12 Maths Chapter 10 talks about types and components of vectors and addition of vectors, multiplication of a vector by a scalar, product of two vectors, projection of a vector on a line and cross product of two vectors. Embibe offers around 400+ practice questions for the students to become efficient in Chapter 10. Students must practice all the questions provided by Embibe thoroughly to perform well in the exams. Scroll down to access the solutions for Chapter 10 Maths.

Vector Algebra is one of the most interesting chapters of all. Practicing all the questions in the textbook and questions provided by Embibe helps students to score good marks in the exams. Although the topic may seem a bit difficult at first, consistent practice teaches interest among the students. The more questions students try to solve, the more efficient they can become in the topic.

All the solutions provided for each question of Class 12 Maths Chapter 10 are based on the latest syllabus. Students can practice all the questions for free. Also, students can access NCERT 3D Videos, NCERT Exemplars, Embibe Explainers, etc., for free.

Below we have provided the list of topics included in Class 12 Maths Chapter 10:

S.No | Topics |
---|---|

1 | Basics of Vectors |

2 | Addition of Vectors |

3 | Multiplication of a Vector by a Scalar |

4 | Product of Vectors |

In our day-to-day life, we come across many queries such as – What is your height? How should a football player hit the ball to give a pass to another player on his team? Observe that a possible answer to the first query maybe 1.6 metres, a quantity that involves only one value (magnitude) which is a real number. Such quantities are called scalars.

However, an answer to the second query is a quantity (called force) which involves muscular strength (magnitude) and direction (in which another player is positioned). Such quantities are called vectors. Below mentioned are some important points of Vector Algebra that should be remembered.

- Co-linear vectors: Two non-zero vectors a→ and b→ are collinear if there exist non-zero scalars x and y such that xa→+yb→=0→.
- Any two non-zero, non-collinear vectors are linearly independent.
- Any two collinear vectors are linearly dependent.
- Any three non-coplanar vectors are linearly independent.
- Any three coplanar vectors are linearly dependent.
- Centroid of a triangle: If S is any point in the plane of a triangle ABC, then SA−→+SB−→+SC−→=3SG−→, where G is the centroid of ∆ABC
- If
*a*→,*b*→,*c*→a→,b→,c→ are three given non-coplanar vectors, then every vector*r*→r→ in space can be uniquely expressed as*r*→=*xa*→+*yb*→+*zc*→r→=xa→+yb→+zc→ for some scalars*x*,*y*x, y and*z*z.

The detailed NCERT Class 12 Maths solutions are provided below for student’s reference:

- Chapter 1: Relations and Functions
- Chapter 2: Inverse Trigonometric Functions
- Chapter 4: Determinants
- Chapter 5: Continuity and Differentiability
- Chapter 6: Applications of Derivatives
- Chapter 7: Integrals
- Chapter 8: Application of Integrals
- Chapter 9: Differential Equations
- Chapter 10: Vector Algebra
- Chapter 11: Three Dimensional Geometry
- Chapter 12: Linear Programming
- Chapter 13: Probability

**Q.1: What are the exercises discussed in NCERT Solutions for Class 12 Maths Chapter 10?****Ans**: The main topics of NCERT Solutions for Class 12 Maths Chapter 10 are Introduction, Basic Concepts, Types of Vectors, Addition of Vectors, Multiplication of a vector by a scalar and Product of Two Vectors.

**Q.2: Where can I get NCERT Solutions for Class 12 Maths for all chapters?****Ans: **You can get NCERT Solutions For Class 12 Maths from this page of Embibe.

**Q.3: How many exercises are there in NCERT Solutions for Class 12 Maths Chapter 10?****Ans: **There are a total of 6 exercises with subtopics in NCERT Solutions for Class 12 Maths Chapter 10.

**Q.4: What is Zero Vector in Class 12 Maths?****Ans: **A vector with a magnitude of 0 is called a zero vector. Here the initial and terminating point of the vector co-occurs together and thus give no direction.

**Q.5: What are the benefits of solving NCERT Solutions for Class 12 Maths Chapter 10 from Embibe?****Ans: **By practising NCERT solutions for Class 12 Maths Chapter 10 from Embibe, students can understand the step-wise approach to solving the problems. Also, students will develop the speed and accuracy of problem-solving. They can build self-confidence to tackle any type of question asked in the exam.