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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.

Read in the blogs more about the unique learning experience at nubtrek.continue

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

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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`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`
  • `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`.

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`.

slide-show version coming soon