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Thought-Process to Discover Knowledge
Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.
In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.
Read in the blogs more about the unique learning experience at nubtrek.continue
Vector Algebra
Welcome to the only place where the essence of vectors is explained.
• A vector in first-principles is a quantity with spatial-direction specified. Example: `2m` north-east.
• A vector in component form is linear-combination of unit vectors of independent directions. eg: `2i+2j`
• A vector in 3D co-ordinate system is a ray initiating from the origin.
Vector addition, dot product, and cross product are explained in
» first principle,
» geometrical meaning, and
» component form.
The details explained here are revolutionary and astonishingly simple to understand.
(click for the list of lessons in this topic)
Introduction to Vector Quantities
Welcome to the only place where the essence of vectors is explained.
Integers are "directed-whole-numbers", with positive numbers aligned to a chosen direction, and negative numbers opposed to the chosen direction.
Vectors are "spatial-directed-quantities". The spatial directions are
• x-axis (eg: right and left for a person)
• y-axis (eg: forward and backward for a person) and
• z-axis (eg: up and down for a person)
This page introduces the concept of vectors and the representation in component form in a simple thought-process.
Properties of Vectors
Welcome to the astoundingly clear and simple lesson on basic properties of vectors.
This topic discusses magnitude of a vector and the properties of that. This also discusses the different types of vectors like null, proper, collinear, coplanar, etc.
The pages in this lesson are
Vectors and Coordinate Geometry
Welcome to the astoundingly clear and simple lesson on vectors and coordinate geometry.
Coordinate Geometry is the system of geometry where the position of points on the 3D coordinates are described as ordered pairs of numbers corresponding to the three axes. In the mathematical representation of vectors, the components along 3D coordinates are described individually. In this topic, you will learn how these two are related.
Direction - Unique Feature of Vectors
Welcome to the only place where the essence of vector arithmetics is explained.
Vectors are quantities with spatial-direction specified.
If two vectors interact, then usually, one vector is split into two components
• component along the direction of the other vector
• component perpendicular to the direction of the other vector.
In vector arithmetics these two components behave differently.
• Vector addition: the component along the direction adds in magnitude.
• Vector dot-product: the component along the direction takes part in the product and the component in perpendicular is lost.
• Vector cross-product: the component in perpendicular to the direction takes part and the component along the direction is lost.
This explanation is coherent and simple for students to connect and remember.
Vector Addition
Welcome to the only place where essence of vector addition is explained.
• vector addition in first-principles: components aligned to each other add.
• component form of vector addition: individual components add independently.
• triangular law: sequential addition of vectors
• parallelogram law: continuous addition of vectors
The details in these pages provide powerful and clear insights.
The pages in this lesson are
Vector Addition - First principles redo
Multiplication of Vectors by Scalar
Welcome to the only place where essence of scalar multiplication of vectors is explained. The following are covered.
• Scalar multiplication of vector
• Standard unit vectors
• Representing a vector as a linear combination of multiple vectors
• Revisiting component form of vectors as linear combination of standard unit vectors
The details in these pages provide powerful and clear insights.
Vector Dot Product
Welcome to the only place where essence of vector dot product is explained. The following are covered.
• Multiplication of two vectors : either component in parallel take part or the component in perpendicular take part
• Vector dot product in first principles
• Projection form of vector dot product
• Component form of vector dot product
The details in these pages provide powerful and clear insights.
Vector Cross Product
Welcome to the only place where essence of vector cross product is explained. The following are covered.
• Multiplication of two vectors : either component in parallel take part or the component in perpendicular take part
• Vector cross product in first principles
• Area of Parallelogram form of vector cross product
• Component form of vector cross product
The details in these pages provide powerful and clear insights.