Vectors

Vectors explained with definitions, operations, direction ratios, dot and cross products, and simple geometric examples.

1.Introduction to Vectors
Learn the basics of vectors with simple notes on scalar vs vector quantities, representation, equality of vectors, and intuitive geometric examples.
2.Direction and Magnitude of a Vector
Learn how to find the magnitude and direction of a vector, understand unit vectors, and use direction ratios and direction cosines with simple examples.
3.Types of Vectors
Understand different types of vectors such as zero vectors, unit vectors, collinear vectors, parallel vectors, and more with simple explanations and examples.
4.Zero Vector
Understand the zero vector with simple notes on its definition, properties, notation, and intuitive examples.
5.Unit Vector
Learn what a unit vector is, how to compute it, and why it is useful in representing direction, with simple formulas and examples.
6.Like and Unlike Vectors
Understand like and unlike vectors with simple explanations, properties, and clear examples that show how their directions relate.
7.Collinear and Non-Collinear Vectors
Understand collinear and non-collinear vectors with clear explanations, simple notes-style definitions, and easy geometric examples.
8.Parallel and Anti-Parallel Vectors
Learn the meaning of parallel and anti-parallel vectors with simple definitions, clear notes-style explanations, and easy geometric examples.
9.Co-Initial and Co-Terminal Vectors
Learn the meaning of co-initial and co-terminal vectors with clear notes-style explanations, simple definitions, and easy geometric examples.
10.Position Vector
Learn what a position vector is, how it represents the location of a point, and how to write it in coordinate form using simple explanations and examples.
11.Addition of Vectors
Learn how to add vectors using the triangle rule, parallelogram rule, and component-wise addition, with simple notes and intuitive examples.
12.Scalar Multiplication of Vectors
Understand how multiplying a vector by a scalar affects its magnitude and direction, with clear explanations and simple examples.
13.Dot Product of Vectors
Understand the dot product of vectors with simple notes: definition, geometric meaning, formulas, properties, and step-by-step examples.
14.Cross Product of Vectors
Learn the cross product of vectors with simple notes: definition, right-hand rule, geometric meaning, determinant formula, and easy examples.
15.Section Formula (Vector Form)
Learn the section formula in vector form to find the position vector of a point dividing a line segment internally or externally in a given ratio, with simple explanations and examples.