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Thought-Process to Discover Knowledge
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)
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.