Class 12th Math Vector Algebra NCERT Solution CBSE 2023
Launch Your Course Log in Sign up
Competitive Exam
Class Notes
Graduate Courses
Job Preparation
vidyakul X

NCERT Solutions for Class 12 Maths Chapter 10

Chapter 10 Vector Algebra

Chapter 12 Mathematical Vector Algebra notes chapter will help students understand the basic concepts related to the subject. This set of notes includes all the questions mentioned in the exercise and detailed notes to vector algebraic formulas. Students preparing for CBSE 12 Board and JEE or other engineering-based entrance exams can refer to this set of notes.

CBSE Grade 12 Math Chapter 10 talks about types and components of vectors and vector addition, vector multiplication with a scalar, product of two vectors, projection of vector onto a line and product of two vectors. Students must practice thoroughly all the questions provided by Vidyakul to do well on the tests. Scroll down to see Chapter 10 Math notes .


Points to Remember

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, yx, y and zz.



Topics and Sub-topics

Vector algebra is one of the most interesting chapters. Practicing all the questions in the textbook and the questions provided by Vidyakul helps students achieve good test scores. Although the subject may seem a bit difficult at first, continuous practice will keep students interested. The more questions students try to solve, the more effective they can become in the subject.

All notes for each question in Chapter 10 of Grade 12 Math are compiled according to the most recent outline. 

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




Basics of Vectors


Addition of Vectors


Multiplication of a Vector by a Scalar


Product of Vectors


Download this solution for FREE Download this PDF