Vector Algebra Class 12 CBSE Maths Chapter 10

Vector Algebra Class 12 CBSE Maths

Class 12 CBSE Maths Syllabus
Chapter 1: Relations and Functions
Chapter 2: Inverse Trigonometric Functions
Chapter 3: Matrices
Chapter 4: Determinants
Chapter 5: Continuity and Differentiability
Chapter 6: Applications of Derivatives
Chapter 7: Integrals
Chapter 8: Applications of Integrals
Chapter 9: Differential Equations
Chapter 10: Vector Algebra
Chapter 11:3D Geometry
Chapter 12: Linear Programming
Chapter 13: Probability

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.