Vector Algebra is a very important chapter in Class 12 Mathematics. It is all about the study of vectors and scalars. There are many quantities in the real world which involve the magnitude as well as direction. If the quantity is having magnitude as well as the direction, then we know as the vectors. We refer such quantities as the Vector Quantities. For example, displacement, velocity, acceleration, force, weight, momentum, electric intensity and many more. Vector algebra chapter will deal with many such quantities and their related theorem and formulas. Thus, vector algebra formulas will create the basic knowledge about the vector terms and their properties.
The concept of vectors is useful to describe the physical quantities having directions and magnitude associated with them. A scalar is a physical quantity that is completely described by a constant or a single numerical value. Vector algebra for class 12 maths chapter 10 includes many important concepts from this topic. Some such topics are vector types, operations, etc. The key points which the chapter covers are vector introduction, types of vectors, and operations on vectors like addition.
The student will learn the scalar or vector and their graphical displacement. Also, they will learn various operations on vectors and many types of vectors such as equal vectors, unit vector, They learn the direction cosines and ratios, section formula, collinearity of two vectors, collinearity of 3 position vectors also.
Some important topics in this chapter are some Basic Concepts, Types of Vectors, Addition 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
The student will study the scalar components of vectors such as direction ratios, its projections along the respective axes. Students will see various types of vectors such as zero or null vector, unit vector, free vectors, negative of a vector, like and unlike vectors, collinear or parallel vectors, etc. Some other types are coinitial vectors, coterminous vectors, localized vectors, coplanar vectors, reciprocal of a vector. The chapter also explains about triangle law of addition of vectors, parallelogram law of addition of vectors, its properties, and subtraction of vectors. Students will learn the methods for multiplication of a given Vector by a Scalar as well as about the product of two vectors with properties.
The chapter will explain the concepts of components of vectors, direction, ratios, and magnitude. The student will learn methods about vector joining two-point and solve them, study to calculate position vectors by dividing the vector internally and externally by section formula. Various properties for the distributivity of scalar product over addition, scalar product is defined by the cosine of the angle formed between two vectors. The projection of a vector on a line is also important to understand. Such lines are making the angle of cosine with an anticlockwise direction. Thus this chapter is really interesting and essential for further study in math as well as Physics.