# Vector Algebra For Class 12

Vector Algebra for class 12 is all about the study of vectors and scalars. There are various quantities, which involves magnitude as well as direction. If the quantity that has magnitude, as well as direction, is known as vectors. Such quantities are known as Vector Quantities. Eg. Displacement, velocity, acceleration, force, weight, momentum, electric intensity etc.

## Vector Algebra for Class 12 Concepts

The concept of vectors is used to describe the physical quantities having directions and magnitude associated with them. A scalar is a physical quantity which is completely described by a constant or a single number. Vector algebra for class 12,  NCERT maths chapter 10 includes various important concepts from this topic like vector types, operations, etc. In this lesson, the key points that are covered from this class 12 Maths vector algebra chapter include vector introduction, types of vectors, and operations on vectors like addition. The topics and sub-topics covered in class 12 are:

• Introduction
• Some Basic Concepts
• Types of Vectors
• Multiplication of a Vector by a Scalar
• Components of a vector
• Vector joining two points
• Section formula
• Product of Two Vectors
• Scalar (or dot) product of two vectors
• Projection of a vector on a line
• Vector (or cross) product of two vectors

## Vector Algebra for Class 12 Notes

In vector algebra for class 12, some basic concepts of vectors like position vectors and the relationship between magnitude, direction ratios and direction cosines are explained in detail.

Position Vector

The position vector is given with respect to the origin O (0,0,0), where the coordinate of point (say P) is P(x,y,z) is given as-

$\overline{OP} = \sqrt{x^{2} + y^{2} + z^{2}}$

Relationship Between Magnitude, Direction Ratios and direction cosines

The magnitude (r), direction ratios (a, b, c) and direction cosines (l, m, n) of any vector are related as l=(a/r), m=(b/r) n=(c/r)

Types of Vectors

The various types of vectors included in vector algebra for class 12 concepts are

(i) Zero Vector

(ii) Unit Vector

(iii) Coinitial Vectors

(iv) Collinear Vectors

(v) Equal Vectors

(vi) Negative of a Vector

Operations on Vectors

In class 12, Chapter 10 Vector Algebra includes addition, subtraction, and three types of multiplication between vectors. Below we will see how to perform addition on two vectors.

$\overline{AC} = \overline{AB} + \overline{BC}$