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Thought-Process to Discover Knowledge

Welcome to nubtrek.

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.

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User Guide   

Welcome to nubtrek.

The content is presented in small-focused learning units to enable you to
  think,
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  learn.

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User Guide   

To make best use of nubtrek, understand what is available.

nubtrek is designed to explain mathematics and science for young readers. Every topic consists of four sections.

  nub,

  trek,

  jogger,

  exercise.

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User Guide    

nub is the simple explanation of the concept.

This captures the small-core of concept in simple-plain English. The objective is to make the learner to think about. continue

User Guide    

trek is the step by step exploration of the concept.

Trekking is bit hard, requiring one to sweat and exert. The benefits of taking the steps are awesome. In the trek, concepts are explained with exploratory questions and your thinking process is honed step by step. continue

User Guide    

jogger provides the complete mathematical definition of the concepts.

This captures the essence of learning and helps one to review at a later point. The reference is available in pdf document too. This is designed to be viewed in a smart-phone screen. continue

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exercise provides practice problems to become fluent in the concepts.

This part does not have much content as of now. Over time, when resources are available, this section will have curated and exam-prep focused questions to test your knowledge. continue

summary of this topic

Multiplication of Vectors by Scalar

Multiplication of Vectors by Scalar

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Standard Unit Vectors


 »  `3` orthogonal axes are represented with `3` unit vectors
    →  x-axis `i`
    →  y-axis `j`
    →  z-axis `k`

Standard Unit Vectors

plain and simple summary

nub

plain and simple summary

nub

dummy

3D vector space is of 3 orthogonal axes, with standard unit vectors `i`, `j`, `k`.

simple steps to build the foundation

trek

simple steps to build the foundation

trek

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In this page, orthogonal axes of vector space and the standard unit vectors are explained.


Keep tapping on the content to continue learning.
Starting on learning "Standard Unit Vectors". ;; In this page, orthogonal axes of vector space and the standard unit vectors are explained.

A person walks `5`m east and then takes the following path

 •  `3`m north

 •  `4.2`m south

 •  `3/4` m north

At this position, how far is the person away from the starting point in the east direction ?

  • `5`m
  • `5+3+4.2+3/4`m
  • `5+3-4.2+3/4`m
  • none of the above

Answer is '`5`m '– as the person moved `5` meter east and then all his movements were in directions north and south.

Any change in a direction affects the component along that direction only and does not affect the components in the directions at `90^@` to that direction.

Independence of Quantities along orthogonal directions: For a vector, changes along one axis affect only the component along that axis and do not affect the components along other axes, as the axes are orthogonal.

How many orthogonal components are there in 3D coordinate space?

  • `1`
  • `2`
  • `3`
  • `4`

The answer is '`3`'. There are 3 orthogonal axes.

Along the three orthogonal axes, irreducible unit is defined as unit vectors `i`, `j`, and `k`.

comprehensive information for quick review

Jogger

comprehensive information for quick review

Jogger

dummy

Standard Unit Vectors: 3D vector space has three orthogonal axes. Unit vectors along the axes are standard unit vectors and are represented with `i`, `j`, and `k`.



           

practice questions to master the knowledge

Exercise

practice questions to master the knowledge

Exercise

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Progress

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Progress

A person walks 5 meter east and then takes the following path ;; 3 meter north;; 4 point 2 meter south ;; 3 by 4 meter north;; At this position, how far is the person away from the starting point in the east direction?
1
2
3
4
The answer is "5 meter", as the person moved 5 meter east and then all his movements were in directions north and south.
Any change in a direction affects the component along that direction only and does not affect the components in the directions at 90 degree to that direction.
Independence of Quantities along orthogonal directions: For a vector, changes along one axis affect only the component along that axis and do not affect the components along other axes, as the axes are orthogonal.
How many orthogonal components are there in 3D coordinate space?
1
1
2
2
3
3
4
4
The answer is ' 3 '. There are 3 orthogonal axes.
Along the three orthogonal axes, irreducible unit is defined as unit vectors i, j, and k
3D vector space is of 3 orthogonal axes, with standard unit vectors i, j, k.
Standard Unit Vectors: 3D vector space has three orthogonal axes. Unit vectors along the axes are standard unit vectors and are represented with i, j, and k

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