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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
mathsVector AlgebraProperties of Dot Product

Dot product of Orthogonal Vectors

In this page, you will learn about the result of vector dot product of orthogonal vectors.



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When are two vectors called 'orthogonal' vectors?orthogonal vectors `color(coral)(text(orth)) + color(deepskyblue)(text(gonia))` means `color(coral)(text(right))+color(deepskyblue)(text(angled))`.

  • have `90^@` angle between them
  • perpendicular to each other
  • the vectors are right-angled
  • all the above
  • all the above

The answer is 'All the above'

Given the definition of dot product as
`vec p cdot vec q = |vec p||vec q|cos theta`
Dot product of orthogonal vectors What is `vec p cdot vec q`, when the given vectors are orthogonal?

  • `|p||q|cos 90`
  • `|p||q| 0`
  • `0`
  • all the above
  • all the above

The answer is 'All the above'.

Given two non-zero vectors `vec p, vec q in bbb V` have `vec p cdot vec q = 0`, then what is the angle between the vectors?

  • `0^@`
  • `90^@`
  • `90^@`
  • `180^@`
  • Any one of the above

The answer is '`90^@`'. It can either be `90^@` or `270^@`.

 •  Dot product of orthogonal vectors is `0`.
    If dot product of two non-zero vectors is `0`, then the vectors are orthogonal.

Dot Product of Orthogonal Vectors: For any pair of orthogonal vectors `vec p, vec q in bbb V`,
`vec p cdot vec q = 0`

Angle between vectors when dot product is `0`: For any pair of non-zero vectors `vec p, vec q in bbb V`, If `vec p cdot vec q = 0` then the vectors are orthogonal. The angle between them is `+- 90^@`.

Solved Exercise Problem:

Given `vec p= 2i+j-k` and `vec q = i+2j+4k` what is the angle between them?

  • `90^@`
  • `90^@`
  • `0`
  • `180^@`
  • `0^@`

The answer is '`90^@`'. As the dot product between the vectors is `0`.

Solved Exercise Problem:

Given two vectors `vec p` and `vec q` in x-y plane. They make angles `13^@` and `-77^@` with x-axis. What is `vec p cdot vec q`?

  • `90`
  • `0`
  • `0`
  • `13xx77`
  • `13xx(-77)`

The answer is '`0`'. The vectors are orthogonal as the angle between them is `13+77`. Note that the vectors are in x-y plane.

                            
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